# clear env
rm(list=ls())

# Load packages
library(car)
library(tidyverse)
library(MASS)
library(DiscriMiner)
library(klaR)
#library(aplpack)
library(fpc)
library(cluster)
library(ape)
library(amap)

# Packages pertinent to Ordination
library(vegan) # eggplant
#library(vegan3d)
library(mgcv)
#library(rgl)
library(dplyr)
library(magrittr)

Contributors

Evan Collins ()

Kelly Farley ()

Ken Stier ()

The Dataset

Raw dataset: COVID-19 infection and death statistics from U.S. counties (sourced from NYT), combined with economic, education, and population data (sourced from various government agencies) and also survey responses about mask-wearing frequencies (sourced from NYT). 3141 complete observations on 19 metric variables and 6 categorical variables. To avoid any outliers due to population size differences between counties, all variables are scaled as a percentage of population. Variable descriptions can be found here.

Data of relevance for this pset:

This pset only explores the 67 counties in the best state, Florida.

We look at five continuous variables describing each county: Always_Wear_Mask_Survey, Median_Household_Income_Percent_of_State_Total_2019, Percent_Poverty_2019, Percent_Adults_Less_Than_HS, and Covid_Confirmed_Cases_as_pct. Note that Always_Wear_Mask_Survey and Covid_Confirmed_Cases_as_pct were multiplied by 100 to convert the value from a fraction to percent value (like the other variables). This data is stored in data_ord_base.

For additional continuous variables, we make an environmental dataset. We look at five additional continuous variables describing each county: Unemployment_Rate_2019, Death_Rate_2019, Birth_Rate_2019, Civilian_Labor_Force_2019_as_pct, Percent_Adults_Bachelors_or_Higher. Note that Civilian_Labor_Force_2019_as_pct was multiplied by 100 to convert the value from a fraction to percent value (like the other variables). This data is stored in data_ord_env.

# Process raw dataset as we have done in preceding psets

raw <- read.csv("https://evancollins.com/covid_and_demographics.csv")

# create categorical variables: rural-urban code (3 levels), region (4 variables)

# log transformations of our continuous variables
raw$logMedian_Household_Income_2019 <- log(raw$Median_Household_Income_2019 + 0.0001)
raw$logPercent_Poverty_2019 <- log(raw$Percent_Poverty_2019 + 0.0001)
raw$logCovid_Confirmed_Cases_as_pct <- log(raw$Covid_Confirmed_Cases_as_pct + 0.0001)
# Base dataset of interest for this pset - data_ord_base
data_ord <- raw[raw$State_Name=="Florida", ]
data_ord <- data_ord[, c(2, 9, 12, 13, 14, 22)]

data_ord_base <- data_ord
data_ord_base$Covid_Confirmed_Cases_as_pct <- 100*data_ord_base$Covid_Confirmed_Cases_as_pct
data_ord_base$Always_Wear_Mask_Survey <- 100*data_ord_base$Always_Wear_Mask_Survey

data_ord_base1 <- data_ord_base
data_ord_base <- data_ord_base1[,-1]
rownames(data_ord_base) <- data_ord_base1[,1] # rownames are county names

dim(data_ord_base)
## [1] 67  5
head(data_ord_base)
##          Always_Wear_Mask_Survey
## Alachua                     75.1
## Baker                       44.2
## Bay                         54.8
## Bradford                    38.1
## Brevard                     60.7
## Broward                     79.1
##          Median_Household_Income_Percent_of_State_Total_2019
## Alachua                                                 84.3
## Baker                                                  102.1
## Bay                                                     98.6
## Bradford                                                80.3
## Brevard                                                 97.3
## Broward                                                103.8
##          Percent_Poverty_2019 Percent_Adults_Less_Than_HS
## Alachua                  18.4                         7.6
## Baker                    14.9                        15.5
## Bay                      12.1                         9.7
## Bradford                 21.0                        21.7
## Brevard                   9.4                         8.0
## Broward                  12.3                        11.2
##          Covid_Confirmed_Cases_as_pct
## Alachua                      7.984597
## Baker                       10.838754
## Bay                         10.043788
## Bradford                     9.712422
## Brevard                      5.189537
## Broward                      9.243293
plot(data_ord_base)

# Enviromental variables dataset - data_ord_env
data_ord_env_county <- raw[raw$State_Name=="Florida", ]
data_ord_env_county <- data_ord_env_county[, c(2, 10, 18, 19, 25, 15)]

data_ord_env <- data_ord_env_county
data_ord_env$Civilian_Labor_Force_2019_as_pct <- 100*data_ord_env$Civilian_Labor_Force_2019_as_pct

data_ord_env1 <- data_ord_env
data_ord_env <- data_ord_env1[,-1]
rownames(data_ord_env) <- data_ord_env1[,1] # rownames are county names

dim(data_ord_env)
## [1] 67  5
head(data_ord_env)
##          Unemployment_Rate_2019 Death_Rate_2019 Birth_Rate_2019
## Alachua                     2.9             7.7            10.3
## Baker                       3.1             9.5            11.2
## Bay                         3.9            11.0            12.3
## Bradford                    3.1            12.5            10.2
## Brevard                     3.2            12.5             8.8
## Broward                     3.0             8.2            11.2
##          Civilian_Labor_Force_2019_as_pct Percent_Adults_Bachelors_or_Higher
## Alachua                          51.74526                               42.5
## Baker                            40.57515                               13.4
## Bay                              48.21556                               22.8
## Bradford                         39.22556                               10.6
## Brevard                          47.19508                               29.3
## Broward                          53.28404                               31.9

1

Fit Correspondence Analysis to your data.

All columns of data_ord_base contains the variable data. Correspondence analysis is performed using the cca() function.

# No negative data anyways
# data_ord_base <- data_ord_base[apply(data_ord_base, 1, sum) > 0, ]

#Perform correspondence analysis
data_ord_base_ca <- cca(data_ord_base)

# inertia is measure of departure from ind model; if no relationships from rows and columns; in this case, household income, percent poverty are related; other variables are not so strongly related; if inertia smaller - less structure to data in 5-D 

2

Discuss the inertia, make a two dimensional plot of the first two CA directions.

summary(data_ord_base_ca)
## 
## Call:
## cca(X = data_ord_base) 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total         0.05033          1
## Unconstrained 0.05033          1
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                           CA1      CA2      CA3      CA4
## Eigenvalue            0.03606 0.009955 0.002521 0.001793
## Proportion Explained  0.71649 0.197808 0.050087 0.035616
## Cumulative Proportion 0.71649 0.914297 0.964384 1.000000
## 
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## 
## 
## Species scores
## 
##                                                          CA1      CA2       CA3
## Always_Wear_Mask_Survey                             -0.04389 -0.14340  0.002602
## Median_Household_Income_Percent_of_State_Total_2019 -0.12367  0.07293 -0.005506
## Percent_Poverty_2019                                 0.36607  0.01375  0.119450
## Percent_Adults_Less_Than_HS                          0.43620  0.01442 -0.127072
## Covid_Confirmed_Cases_as_pct                         0.23445  0.14590  0.048594
##                                                          CA4
## Always_Wear_Mask_Survey                              0.01398
## Median_Household_Income_Percent_of_State_Total_2019 -0.01211
## Percent_Poverty_2019                                -0.06152
## Percent_Adults_Less_Than_HS                         -0.01670
## Covid_Confirmed_Cases_as_pct                         0.17146
## 
## 
## Site scores (weighted averages of species scores)
## 
##                     CA1      CA2      CA3       CA4
## Alachua      -0.2579870 -1.60706  2.77217  0.400127
## Baker         0.0280475  1.66967 -0.23324  0.190358
## Bay          -0.5365473  0.59860  0.64355  1.166522
## Bradford      1.2707134  1.41794 -0.27880 -1.401618
## Brevard      -1.0058699 -0.33752 -0.04251 -0.470399
## Broward      -0.6113475 -0.97532  0.23822  1.265977
## Calhoun       1.3900689  0.02428 -0.16307  0.484268
## Charlotte    -0.6966676 -0.74566  0.09810 -0.536160
## Citrus       -0.1394691 -0.75200  0.65413 -0.816689
## Clay         -1.2865849  1.56298 -0.68961 -0.642613
## Collier      -0.9516428  0.62048 -1.37787 -0.424347
## Columbia      0.4255024  1.39936  0.85239  0.584438
## DeSoto        1.4124015 -1.54893 -1.23015 -0.215095
## Dixie         1.5911653  0.66090  0.41171 -1.853031
## Duval        -0.4777867 -0.10803  0.67291  0.565342
## Escambia     -0.1999783  0.46290  1.84232  0.884221
## Flagler      -1.1162511  0.02829 -0.11021 -1.040040
## Franklin      1.0293941  1.18179 -0.08849 -0.391357
## Gadsden       1.1331068 -0.38765  0.06956  1.041970
## Gilchrist     0.2923450  0.49907  0.04248 -1.120320
## Glades        0.9602104 -1.33106 -1.49877 -1.420773
## Gulf          0.2524635  1.27854  0.02130  2.094265
## Hamilton      2.4514005  1.14909  2.54929 -2.856752
## Hardee        1.6243491  0.18401 -0.48894 -0.778705
## Hendry        1.6425587 -0.76661 -3.48737 -0.265267
## Hernando     -0.2998987 -0.60987 -0.40381 -0.858329
## Highlands     0.2519377 -1.18798 -0.01501 -0.567841
## Hillsborough -0.5718720 -0.69371  0.19420 -0.141031
## Holmes        1.4478480 -0.62345 -0.36468  0.727175
## Indian River -0.6894247  0.04277 -0.33385 -0.587752
## Jackson       1.2323901 -0.11028  0.52615  1.685731
## Jefferson     0.5199624 -1.08804  0.05242  0.654107
## Lafayette     1.5911661  1.87293 -0.72446  3.927492
## Lake         -0.6913000 -0.39668 -0.26513 -0.220985
## Lee          -0.6743885 -0.12695 -0.50324 -0.126535
## Leon         -0.2733104 -0.75881  3.57284  0.209794
## Levy          0.6182007 -1.17123  0.61102 -0.978715
## Liberty       1.2580903  0.50200  1.53857  0.360751
## Madison       1.7895438  1.25426  1.29302 -1.010829
## Manatee      -0.7719348  0.15722 -0.19547 -0.142531
## Marion        0.0007508 -0.19202  0.44339 -0.551968
## Martin       -1.1684693 -0.20071 -0.58139 -0.246356
## Miami-Dade    0.2996775 -0.69843 -0.18127  2.816490
## Monroe       -1.0677179 -0.94099  0.03983  0.703280
## Nassau       -1.1748135  1.88767 -0.34885 -0.333700
## Okaloosa     -0.9045129  1.42972  0.35211 -0.007087
## Okeechobee    0.9644400 -1.46129 -1.64082 -0.286844
## Orange       -0.6481869 -0.54586  0.03647  0.195285
## Osceola      -0.1761811 -1.10587  0.15055  1.364315
## Palm Beach   -0.7863143 -0.73505 -0.34040  0.290999
## Pasco        -0.6495546 -1.12949 -0.22874 -0.211219
## Pinellas     -0.7857529 -1.30050  0.41633  0.359708
## Polk         -0.0173068 -0.63077 -0.47020 -0.120923
## Putnam        1.0882213 -0.83097  0.84041 -1.396901
## St. Johns    -1.8246946  1.91832 -0.46595 -0.771806
## St. Lucie    -0.4973983 -0.51158 -1.18380 -0.222083
## Santa Rosa   -0.9793112  1.73872  0.06881  0.120004
## Sarasota     -1.3034658 -0.42690 -0.25311  0.107948
## Seminole     -1.4009072 -0.32091  0.34367 -0.478166
## Sumter       -1.1177304 -0.06506 -0.32542 -0.421412
## Suwannee      0.8290661  1.75865 -0.30903  0.183506
## Taylor        1.4076618  0.46177 -0.43854  0.710780
## Union         1.0743577  0.92255 -0.77718 -0.237763
## Volusia      -0.5157772 -0.59935  0.52913 -0.612641
## Wakulla      -0.3710730  1.56935 -0.22170  0.039781
## Walton       -0.6230454  1.06728 -0.38047  0.383858
## Washington    1.0322373 -0.42952  0.54986  0.195862

Inertia (equal to squared eigenvalues) is like variance and measures departures from the independence model. We see that the inertia value is 0.05033. The magnitude of inertia does not reflect more or less variance per se; it is reflective of the magnitude of the data. (Note that multiplying fractions by 100 to make values as percents did not increase this inertia magnitude).

In the “Proportion Explained” row, we can see that first CA direction explains 0.71649 (~72%) of the relation. The “Cumulative Proportion” by the second CA direction is 0.914297; hence, the first and second CA directions explain the vast majority of total inertia. The third and fourth CA directions have significantly smaller “Proportion Explained” values. This suggests that there are likely two major underlying discriminatory dimensions captured by the data.

#plot results
plot(data_ord_base_ca, main = "Correspondence Analysis for FL Counties", type = "n")
text(data_ord_base_ca, dis = "wa", labels = rownames(data_ord_base))
points(data_ord_base_ca, pch = 21, col = "red", bg = "yellow", cex = 1.2)
text(data_ord_base_ca, "species", col = "blue", cex = 0.8)

Add environmental variables.

plot(data_ord_base_ca, main = "Correspondence Analysis for FL Counties", type = "n")
points(data_ord_base_ca, pch = 19, col = "black", cex = 1)
text(data_ord_base_ca, "species", col = "blue", cex = 1.1)
#add environmental variables
fit <- envfit(data_ord_base_ca, data_ord_env, permutations = 1000)
plot(fit, col = "red", lwd = 3)

#get significance - all environmental variables are significant
fit
## 
## ***VECTORS
## 
##                                         CA1      CA2     r2   Pr(>r)    
## Unemployment_Rate_2019              0.93609 -0.35176 0.2400 0.000999 ***
## Death_Rate_2019                     0.61828 -0.78596 0.0084 0.784216    
## Birth_Rate_2019                     0.99605  0.08877 0.0450 0.228771    
## Civilian_Labor_Force_2019_as_pct   -0.97424 -0.22551 0.4110 0.000999 ***
## Percent_Adults_Bachelors_or_Higher -0.99468 -0.10305 0.6962 0.000999 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 1000

We can see that all environmental variables are significant (p < 0.05) except Birth_Rate_2019 and Death_Rate_2019. We will omit these variables from the environmental variable dataset for future analyses.

data_ord_env <- subset(data_ord_env, select=-2)
data_ord_env <- subset(data_ord_env, select=-2)

This plot is somewhat hard to read, so we try detrended correspondence analysis. This is even harder to read. DCA uses the decorana() function.

#detrended correspondence analysis
data_ord_base_dca <- decorana(data_ord_base)
plot(data_ord_base_dca, main = "DCA for Rural-Urban Type", type = "n")
text(data_ord_base_dca, display = c("sites"), labels = rownames(data_ord_base), cex = 0.86)
points(data_ord_base_dca, pch = 21, col = "red", bg = "yellow", cex = 0.6)
text(data_ord_base_dca, "species", col = "blue", cex = 0.6)

#add environmental variables
fit <- envfit(data_ord_base_dca, data_ord_env, permutations = 1000)
plot(fit, col = "red", lwd = 3)

3

Comment on whether or not there is any evidence of ‘data snaking’ in higher dimensional space.

pc1 <- princomp(data_ord_env, cor=TRUE)

source("http://reuningscherer.net/multivariate/r/ciscoreplot.R.txt")
ciscoreplot(pc1,c(1,2),data_ord_env[,1])
## Warning in sqrt((5.99 - (y1vec^2)/x$sdev[comps[1]]^2) * x$sdev[comps[2]]^2):
## NaNs produced

## Warning in sqrt((5.99 - (y1vec^2)/x$sdev[comps[1]]^2) * x$sdev[comps[2]]^2):
## NaNs produced

There is no evidence of data snaking in higher dimensional space. Evidence of snaking would be a PCA score plot that looks like a horseshoe. However, the above scoreplot appears random and therefore does not indicate data snaking.

4

In a few sentences, describe what you conclude from your plot.

From our first plot in (2) of the first two CA directions, we should be able to find which counties are similar and what are the columns on which they are similar. Overall, the counties seem evenly and randomly scattered between the 4 quadrants- we do not note rows near columns, so there is not association not accounted for by the independence model. Generally, the first correspondence axis is associated with low income and low education and high COVID-19 rates, while the second correspondence axis is associated primarily with poor masking behaviors and high COVID-19 rates, perhaps indicating two different types of counties that are associated with high COVID-19 rates (those in poorer, disadvantaged areas and also those with poor masking behaviors). As one may expect, the percent poverty and percent of adults with less than a high school degree point in the same direction, while the median household income points in the opposite direction.

5

Perform Multidimensional Scaling (metric or non-metric) for 1, 2, and 3 dimensions.

results <- matrix(NA, 21, 5)
#j is number of dimensions to try
for (j in 1:5){
  for (i in 1:20){
    temp <- data_ord_base[shuffle(nrow(data_ord_base)), 1]
    for (k in 2:12) { temp <- cbind(temp, data_ord_base[shuffle(nrow(data_ord_base)), k]) }
    #store stress
    results[i, j] <- metaMDS(temp, k = j, distance = "euclidean")$stress
  }
  results[21, j] <- metaMDS(data_ord_base, k = j, distance = "euclidean")$stress
}
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3943127 
## Run 1 stress 0.568615 
## Run 2 stress 0.4155144 
## Run 3 stress 0.5683427 
## Run 4 stress 0.4823638 
## Run 5 stress 0.4505892 
## Run 6 stress 0.5634953 
## Run 7 stress 0.4540016 
## Run 8 stress 0.4275637 
## Run 9 stress 0.5211749 
## Run 10 stress 0.4309893 
## Run 11 stress 0.5681489 
## Run 12 stress 0.5683828 
## Run 13 stress 0.4647005 
## Run 14 stress 0.4984322 
## Run 15 stress 0.3902451 
## ... New best solution
## ... Procrustes: rmse 0.021273  max resid 0.138805 
## Run 16 stress 0.5267726 
## Run 17 stress 0.5676467 
## Run 18 stress 0.5642802 
## Run 19 stress 0.5684096 
## Run 20 stress 0.5387107 
## *** No convergence -- monoMDS stopping criteria:
##      9: stress ratio > sratmax
##     11: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3822443 
## Run 1 stress 0.5685735 
## Run 2 stress 0.5686648 
## Run 3 stress 0.4390485 
## Run 4 stress 0.5673861 
## Run 5 stress 0.5573369 
## Run 6 stress 0.5682804 
## Run 7 stress 0.4462717 
## Run 8 stress 0.5682225 
## Run 9 stress 0.5685445 
## Run 10 stress 0.5676567 
## Run 11 stress 0.5251719 
## Run 12 stress 0.560842 
## Run 13 stress 0.4679827 
## Run 14 stress 0.5349863 
## Run 15 stress 0.437663 
## Run 16 stress 0.4702736 
## Run 17 stress 0.5614889 
## Run 18 stress 0.438425 
## Run 19 stress 0.5685492 
## Run 20 stress 0.5671231 
## *** No convergence -- monoMDS stopping criteria:
##      4: stress ratio > sratmax
##     16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3757599 
## Run 1 stress 0.5339853 
## Run 2 stress 0.5646727 
## Run 3 stress 0.5411931 
## Run 4 stress 0.5686678 
## Run 5 stress 0.5673905 
## Run 6 stress 0.4747698 
## Run 7 stress 0.5399998 
## Run 8 stress 0.4013165 
## Run 9 stress 0.5670451 
## Run 10 stress 0.4061334 
## Run 11 stress 0.5681209 
## Run 12 stress 0.5679906 
## Run 13 stress 0.5214608 
## Run 14 stress 0.5681227 
## Run 15 stress 0.3790507 
## Run 16 stress 0.3752992 
## ... New best solution
## ... Procrustes: rmse 0.012356  max resid 0.04729131 
## Run 17 stress 0.5683744 
## Run 18 stress 0.5684017 
## Run 19 stress 0.379117 
## Run 20 stress 0.5681329 
## *** No convergence -- monoMDS stopping criteria:
##      4: stress ratio > sratmax
##     16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.375132 
## Run 1 stress 0.4857807 
## Run 2 stress 0.5677602 
## Run 3 stress 0.4879986 
## Run 4 stress 0.4449863 
## Run 5 stress 0.5680326 
## Run 6 stress 0.5685972 
## Run 7 stress 0.5673691 
## Run 8 stress 0.5686677 
## Run 9 stress 0.5681667 
## Run 10 stress 0.4889232 
## Run 11 stress 0.4566322 
## Run 12 stress 0.3758467 
## Run 13 stress 0.5681471 
## Run 14 stress 0.5607571 
## Run 15 stress 0.4460828 
## Run 16 stress 0.5670206 
## Run 17 stress 0.4473818 
## Run 18 stress 0.4237776 
## Run 19 stress 0.4626733 
## Run 20 stress 0.5683772 
## *** No convergence -- monoMDS stopping criteria:
##      6: stress ratio > sratmax
##     14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3667049 
## Run 1 stress 0.5671196 
## Run 2 stress 0.4074365 
## Run 3 stress 0.5681924 
## Run 4 stress 0.5681904 
## Run 5 stress 0.3664824 
## ... New best solution
## ... Procrustes: rmse 0.006984227  max resid 0.03158248 
## Run 6 stress 0.568438 
## Run 7 stress 0.5673793 
## Run 8 stress 0.4409874 
## Run 9 stress 0.5415778 
## Run 10 stress 0.4075634 
## Run 11 stress 0.3661472 
## ... New best solution
## ... Procrustes: rmse 0.007118024  max resid 0.0246053 
## Run 12 stress 0.4158464 
## Run 13 stress 0.4256755 
## Run 14 stress 0.5681009 
## Run 15 stress 0.5668567 
## Run 16 stress 0.567953 
## Run 17 stress 0.3584335 
## ... New best solution
## ... Procrustes: rmse 0.08064193  max resid 0.5662588 
## Run 18 stress 0.4831527 
## Run 19 stress 0.4380623 
## Run 20 stress 0.5453604 
## *** No convergence -- monoMDS stopping criteria:
##      1: stress ratio > sratmax
##     19: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3745206 
## Run 1 stress 0.5654734 
## Run 2 stress 0.5683428 
## Run 3 stress 0.527673 
## Run 4 stress 0.4319327 
## Run 5 stress 0.552586 
## Run 6 stress 0.5677485 
## Run 7 stress 0.4005326 
## Run 8 stress 0.565497 
## Run 9 stress 0.5451122 
## Run 10 stress 0.5670775 
## Run 11 stress 0.5685265 
## Run 12 stress 0.4076209 
## Run 13 stress 0.4304182 
## Run 14 stress 0.5094548 
## Run 15 stress 0.4104833 
## Run 16 stress 0.5620525 
## Run 17 stress 0.4477147 
## Run 18 stress 0.4541433 
## Run 19 stress 0.5629403 
## Run 20 stress 0.4394825 
## *** No convergence -- monoMDS stopping criteria:
##      9: stress ratio > sratmax
##     11: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3826193 
## Run 1 stress 0.3841599 
## Run 2 stress 0.3839553 
## Run 3 stress 0.4314456 
## Run 4 stress 0.4659825 
## Run 5 stress 0.5682937 
## Run 6 stress 0.5237444 
## Run 7 stress 0.4524955 
## Run 8 stress 0.5657742 
## Run 9 stress 0.5682134 
## Run 10 stress 0.5684591 
## Run 11 stress 0.5675152 
## Run 12 stress 0.5003737 
## Run 13 stress 0.5042352 
## Run 14 stress 0.4177035 
## Run 15 stress 0.4826258 
## Run 16 stress 0.5685155 
## Run 17 stress 0.5681768 
## Run 18 stress 0.551974 
## Run 19 stress 0.4774262 
## Run 20 stress 0.5683588 
## *** No convergence -- monoMDS stopping criteria:
##      6: stress ratio > sratmax
##     14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3729636 
## Run 1 stress 0.3877855 
## Run 2 stress 0.5686604 
## Run 3 stress 0.5671266 
## Run 4 stress 0.5598195 
## Run 5 stress 0.3828396 
## Run 6 stress 0.5335957 
## Run 7 stress 0.5679142 
## Run 8 stress 0.5394912 
## Run 9 stress 0.4413787 
## Run 10 stress 0.3837507 
## Run 11 stress 0.4048434 
## Run 12 stress 0.4202791 
## Run 13 stress 0.4811087 
## Run 14 stress 0.5538825 
## Run 15 stress 0.4360175 
## Run 16 stress 0.4666248 
## Run 17 stress 0.5452011 
## Run 18 stress 0.5685286 
## Run 19 stress 0.5684511 
## Run 20 stress 0.5681741 
## *** No convergence -- monoMDS stopping criteria:
##      4: stress ratio > sratmax
##     16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.361473 
## Run 1 stress 0.5674536 
## Run 2 stress 0.3705226 
## Run 3 stress 0.3665008 
## Run 4 stress 0.5251432 
## Run 5 stress 0.4795206 
## Run 6 stress 0.4343672 
## Run 7 stress 0.487786 
## Run 8 stress 0.5064389 
## Run 9 stress 0.491882 
## Run 10 stress 0.45107 
## Run 11 stress 0.5333318 
## Run 12 stress 0.5681508 
## Run 13 stress 0.3614506 
## ... New best solution
## ... Procrustes: rmse 0.01441586  max resid 0.07417966 
## Run 14 stress 0.4489148 
## Run 15 stress 0.5034096 
## Run 16 stress 0.4313909 
## Run 17 stress 0.568115 
## Run 18 stress 0.546872 
## Run 19 stress 0.568506 
## Run 20 stress 0.5682568 
## *** No convergence -- monoMDS stopping criteria:
##      5: stress ratio > sratmax
##     15: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3705003 
## Run 1 stress 0.5680188 
## Run 2 stress 0.4336803 
## Run 3 stress 0.5675581 
## Run 4 stress 0.5334681 
## Run 5 stress 0.4463232 
## Run 6 stress 0.5679463 
## Run 7 stress 0.4302918 
## Run 8 stress 0.5413346 
## Run 9 stress 0.5680125 
## Run 10 stress 0.5683107 
## Run 11 stress 0.5493182 
## Run 12 stress 0.5683157 
## Run 13 stress 0.4614034 
## Run 14 stress 0.4881365 
## Run 15 stress 0.5415326 
## Run 16 stress 0.5684518 
## Run 17 stress 0.5684734 
## Run 18 stress 0.4698176 
## Run 19 stress 0.5625737 
## Run 20 stress 0.5683277 
## *** No convergence -- monoMDS stopping criteria:
##      5: stress ratio > sratmax
##     15: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3670519 
## Run 1 stress 0.4452887 
## Run 2 stress 0.5521815 
## Run 3 stress 0.5034962 
## Run 4 stress 0.5373903 
## Run 5 stress 0.5680686 
## Run 6 stress 0.5678935 
## Run 7 stress 0.5650486 
## Run 8 stress 0.5031836 
## Run 9 stress 0.5654533 
## Run 10 stress 0.5683615 
## Run 11 stress 0.5680942 
## Run 12 stress 0.567856 
## Run 13 stress 0.4923205 
## Run 14 stress 0.5681236 
## Run 15 stress 0.5678589 
## Run 16 stress 0.5685633 
## Run 17 stress 0.5684371 
## Run 18 stress 0.487241 
## Run 19 stress 0.4634158 
## Run 20 stress 0.4784426 
## *** No convergence -- monoMDS stopping criteria:
##      6: stress ratio > sratmax
##     14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3450386 
## Run 1 stress 0.344485 
## ... New best solution
## ... Procrustes: rmse 0.01417213  max resid 0.09609239 
## Run 2 stress 0.5684687 
## Run 3 stress 0.3826649 
## Run 4 stress 0.5679463 
## Run 5 stress 0.5683152 
## Run 6 stress 0.4620363 
## Run 7 stress 0.5675596 
## Run 8 stress 0.4737062 
## Run 9 stress 0.5243276 
## Run 10 stress 0.4159715 
## Run 11 stress 0.3449435 
## ... Procrustes: rmse 0.01669781  max resid 0.1162279 
## Run 12 stress 0.4699551 
## Run 13 stress 0.4732501 
## Run 14 stress 0.5681595 
## Run 15 stress 0.450047 
## Run 16 stress 0.5247535 
## Run 17 stress 0.4594415 
## Run 18 stress 0.348426 
## Run 19 stress 0.4646784 
## Run 20 stress 0.3445707 
## ... Procrustes: rmse 0.003324356  max resid 0.01258696 
## *** No convergence -- monoMDS stopping criteria:
##      7: stress ratio > sratmax
##     13: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3362906 
## Run 1 stress 0.5641808 
## Run 2 stress 0.4483219 
## Run 3 stress 0.3689247 
## Run 4 stress 0.4147439 
## Run 5 stress 0.4991684 
## Run 6 stress 0.481518 
## Run 7 stress 0.5679456 
## Run 8 stress 0.550369 
## Run 9 stress 0.3682479 
## Run 10 stress 0.4711453 
## Run 11 stress 0.4392174 
## Run 12 stress 0.5682475 
## Run 13 stress 0.4684234 
## Run 14 stress 0.5684503 
## Run 15 stress 0.5682988 
## Run 16 stress 0.5651844 
## Run 17 stress 0.3477934 
## Run 18 stress 0.5000595 
## Run 19 stress 0.4544496 
## Run 20 stress 0.5615737 
## *** No convergence -- monoMDS stopping criteria:
##      4: stress ratio > sratmax
##     16: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3765862 
## Run 1 stress 0.5682679 
## Run 2 stress 0.46348 
## Run 3 stress 0.5684387 
## Run 4 stress 0.5684219 
## Run 5 stress 0.5631206 
## Run 6 stress 0.4638351 
## Run 7 stress 0.5678059 
## Run 8 stress 0.4683107 
## Run 9 stress 0.4953187 
## Run 10 stress 0.476029 
## Run 11 stress 0.4563858 
## Run 12 stress 0.5685776 
## Run 13 stress 0.5682353 
## Run 14 stress 0.4950701 
## Run 15 stress 0.3935495 
## Run 16 stress 0.5138507 
## Run 17 stress 0.5686367 
## Run 18 stress 0.3890121 
## Run 19 stress 0.4923203 
## Run 20 stress 0.5672976 
## *** No convergence -- monoMDS stopping criteria:
##      5: stress ratio > sratmax
##     15: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.371102 
## Run 1 stress 0.5531016 
## Run 2 stress 0.4366037 
## Run 3 stress 0.5617704 
## Run 4 stress 0.5684773 
## Run 5 stress 0.5668578 
## Run 6 stress 0.4744586 
## Run 7 stress 0.482361 
## Run 8 stress 0.5169139 
## Run 9 stress 0.5442052 
## Run 10 stress 0.443081 
## Run 11 stress 0.5685282 
## Run 12 stress 0.5684348 
## Run 13 stress 0.5682799 
## Run 14 stress 0.5678955 
## Run 15 stress 0.4256311 
## Run 16 stress 0.5684209 
## Run 17 stress 0.5273724 
## Run 18 stress 0.4855864 
## Run 19 stress 0.5679672 
## Run 20 stress 0.5681544 
## *** No convergence -- monoMDS stopping criteria:
##      7: stress ratio > sratmax
##     13: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.359256 
## Run 1 stress 0.4813914 
## Run 2 stress 0.5461467 
## Run 3 stress 0.4848979 
## Run 4 stress 0.4134307 
## Run 5 stress 0.5384053 
## Run 6 stress 0.5655361 
## Run 7 stress 0.5273532 
## Run 8 stress 0.5679133 
## Run 9 stress 0.4187869 
## Run 10 stress 0.5675576 
## Run 11 stress 0.3590307 
## ... New best solution
## ... Procrustes: rmse 0.0152147  max resid 0.07105711 
## Run 12 stress 0.5683499 
## Run 13 stress 0.5684489 
## Run 14 stress 0.4575188 
## Run 15 stress 0.4267903 
## Run 16 stress 0.568037 
## Run 17 stress 0.4140334 
## Run 18 stress 0.4273241 
## Run 19 stress 0.5453929 
## Run 20 stress 0.5686451 
## *** No convergence -- monoMDS stopping criteria:
##      7: stress ratio > sratmax
##     13: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3420562 
## Run 1 stress 0.467693 
## Run 2 stress 0.3429793 
## Run 3 stress 0.5684956 
## Run 4 stress 0.3607349 
## Run 5 stress 0.5672432 
## Run 6 stress 0.4975214 
## Run 7 stress 0.4188735 
## Run 8 stress 0.3748231 
## Run 9 stress 0.411328 
## Run 10 stress 0.509515 
## Run 11 stress 0.3779407 
## Run 12 stress 0.384394 
## Run 13 stress 0.5682633 
## Run 14 stress 0.5677004 
## Run 15 stress 0.5684026 
## Run 16 stress 0.4033995 
## Run 17 stress 0.5685194 
## Run 18 stress 0.4015719 
## Run 19 stress 0.5682626 
## Run 20 stress 0.4931129 
## *** No convergence -- monoMDS stopping criteria:
##      3: stress ratio > sratmax
##     17: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3646387 
## Run 1 stress 0.5350868 
## Run 2 stress 0.4132157 
## Run 3 stress 0.5672118 
## Run 4 stress 0.4935338 
## Run 5 stress 0.4181702 
## Run 6 stress 0.568152 
## Run 7 stress 0.3648739 
## ... Procrustes: rmse 0.004311933  max resid 0.02726331 
## Run 8 stress 0.4974078 
## Run 9 stress 0.4914274 
## Run 10 stress 0.4158754 
## Run 11 stress 0.5661599 
## Run 12 stress 0.4701289 
## Run 13 stress 0.5684419 
## Run 14 stress 0.5660656 
## Run 15 stress 0.4860794 
## Run 16 stress 0.5682188 
## Run 17 stress 0.5679819 
## Run 18 stress 0.3646933 
## ... Procrustes: rmse 0.005048529  max resid 0.01992711 
## Run 19 stress 0.5686356 
## Run 20 stress 0.5681808 
## *** No convergence -- monoMDS stopping criteria:
##      6: stress ratio > sratmax
##     14: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.3501299 
## Run 1 stress 0.5674703 
## Run 2 stress 0.5684262 
## Run 3 stress 0.5682873 
## Run 4 stress 0.3564945 
## Run 5 stress 0.5668782 
## Run 6 stress 0.5548761 
## Run 7 stress 0.4908984 
## Run 8 stress 0.5674929 
## Run 9 stress 0.5681265 
## Run 10 stress 0.5619067 
## Run 11 stress 0.5680905 
## Run 12 stress 0.5232781 
## Run 13 stress 0.3673538 
## Run 14 stress 0.5683727 
## Run 15 stress 0.4172845 
## Run 16 stress 0.4510423 
## Run 17 stress 0.5682977 
## Run 18 stress 0.5683414 
## Run 19 stress 0.5665338 
## Run 20 stress 0.4591338 
## *** No convergence -- monoMDS stopping criteria:
##      2: stress ratio > sratmax
##     18: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.4032906 
## Run 1 stress 0.4106769 
## Run 2 stress 0.5683403 
## Run 3 stress 0.5678662 
## Run 4 stress 0.5684957 
## Run 5 stress 0.4250176 
## Run 6 stress 0.4191311 
## Run 7 stress 0.4427645 
## Run 8 stress 0.5677323 
## Run 9 stress 0.5686239 
## Run 10 stress 0.5680608 
## Run 11 stress 0.4286555 
## Run 12 stress 0.5685516 
## Run 13 stress 0.4791662 
## Run 14 stress 0.5684969 
## Run 15 stress 0.4572891 
## Run 16 stress 0.4517909 
## Run 17 stress 0.4630738 
## Run 18 stress 0.5686066 
## Run 19 stress 0.5686678 
## Run 20 stress 0.4448143 
## *** No convergence -- monoMDS stopping criteria:
##      3: stress ratio > sratmax
##     17: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1901664 
## Run 1 stress 0.5657643 
## Run 2 stress 0.5636877 
## Run 3 stress 0.1897935 
## ... New best solution
## ... Procrustes: rmse 0.008534418  max resid 0.05961287 
## Run 4 stress 0.1897189 
## ... New best solution
## ... Procrustes: rmse 0.002473722  max resid 0.01098358 
## Run 5 stress 0.5685319 
## Run 6 stress 0.544491 
## Run 7 stress 0.2737205 
## Run 8 stress 0.190344 
## Run 9 stress 0.4582411 
## Run 10 stress 0.1902855 
## Run 11 stress 0.510432 
## Run 12 stress 0.5624999 
## Run 13 stress 0.2765784 
## Run 14 stress 0.2755697 
## Run 15 stress 0.1899135 
## ... Procrustes: rmse 0.003664034  max resid 0.01813173 
## Run 16 stress 0.557042 
## Run 17 stress 0.5551162 
## Run 18 stress 0.5683189 
## Run 19 stress 0.1898422 
## ... Procrustes: rmse 0.00198652  max resid 0.00995406 
## ... Similar to previous best
## Run 20 stress 0.5676039 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1815256 
## Run 1 stress 0.1816058 
## ... Procrustes: rmse 0.005145445  max resid 0.0373673 
## Run 2 stress 0.1824844 
## Run 3 stress 0.1824844 
## Run 4 stress 0.1819584 
## ... Procrustes: rmse 0.03454869  max resid 0.2670509 
## Run 5 stress 0.1816064 
## ... Procrustes: rmse 0.005138434  max resid 0.03730599 
## Run 6 stress 0.1819576 
## ... Procrustes: rmse 0.03443718  max resid 0.2669919 
## Run 7 stress 0.1819575 
## ... Procrustes: rmse 0.03444723  max resid 0.2669882 
## Run 8 stress 0.1816058 
## ... Procrustes: rmse 0.005130142  max resid 0.03726707 
## Run 9 stress 0.1816058 
## ... Procrustes: rmse 0.005143062  max resid 0.03735822 
## Run 10 stress 0.1815256 
## ... New best solution
## ... Procrustes: rmse 2.011378e-05  max resid 8.165248e-05 
## ... Similar to previous best
## Run 11 stress 0.1824965 
## Run 12 stress 0.1819577 
## ... Procrustes: rmse 0.03443266  max resid 0.2669996 
## Run 13 stress 0.1815257 
## ... Procrustes: rmse 6.470238e-05  max resid 0.0003762505 
## ... Similar to previous best
## Run 14 stress 0.1833 
## Run 15 stress 0.1816059 
## ... Procrustes: rmse 0.005137459  max resid 0.0373192 
## Run 16 stress 0.1819578 
## ... Procrustes: rmse 0.03450049  max resid 0.2670379 
## Run 17 stress 0.1815257 
## ... Procrustes: rmse 8.186038e-05  max resid 0.0004277621 
## ... Similar to previous best
## Run 18 stress 0.181606 
## ... Procrustes: rmse 0.005150956  max resid 0.03740907 
## Run 19 stress 0.2056097 
## Run 20 stress 0.1824844 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1896778 
## Run 1 stress 0.1884253 
## ... New best solution
## ... Procrustes: rmse 0.02282997  max resid 0.1761241 
## Run 2 stress 0.2004506 
## Run 3 stress 0.1914619 
## Run 4 stress 0.2005318 
## Run 5 stress 0.1891668 
## Run 6 stress 0.1893407 
## Run 7 stress 0.2321239 
## Run 8 stress 0.1904069 
## Run 9 stress 0.1884426 
## ... Procrustes: rmse 0.002276795  max resid 0.01437376 
## Run 10 stress 0.1888497 
## ... Procrustes: rmse 0.0114335  max resid 0.08532459 
## Run 11 stress 0.2005318 
## Run 12 stress 0.1893411 
## Run 13 stress 0.1914768 
## Run 14 stress 0.2005317 
## Run 15 stress 0.1889407 
## Run 16 stress 0.1904066 
## Run 17 stress 0.1884469 
## ... Procrustes: rmse 0.02907987  max resid 0.1875463 
## Run 18 stress 0.1884446 
## ... Procrustes: rmse 0.02922003  max resid 0.1879458 
## Run 19 stress 0.18885 
## ... Procrustes: rmse 0.01151651  max resid 0.08603751 
## Run 20 stress 0.1891666 
## *** No convergence -- monoMDS stopping criteria:
##     19: stress ratio > sratmax
##      1: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1864124 
## Run 1 stress 0.1911627 
## Run 2 stress 0.2163852 
## Run 3 stress 0.1840202 
## ... New best solution
## ... Procrustes: rmse 0.03594734  max resid 0.2294318 
## Run 4 stress 0.1865746 
## Run 5 stress 0.1958795 
## Run 6 stress 0.2089148 
## Run 7 stress 0.1869208 
## Run 8 stress 0.1844912 
## ... Procrustes: rmse 0.01940025  max resid 0.0783345 
## Run 9 stress 0.1840013 
## ... New best solution
## ... Procrustes: rmse 0.005212787  max resid 0.02364139 
## Run 10 stress 0.2190791 
## Run 11 stress 0.406593 
## Run 12 stress 0.184378 
## ... Procrustes: rmse 0.01776723  max resid 0.08400709 
## Run 13 stress 0.1911629 
## Run 14 stress 0.1921569 
## Run 15 stress 0.1911629 
## Run 16 stress 0.1926636 
## Run 17 stress 0.203463 
## Run 18 stress 0.1921569 
## Run 19 stress 0.1926629 
## Run 20 stress 0.1958946 
## *** No convergence -- monoMDS stopping criteria:
##     20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.187465 
## Run 1 stress 0.2105465 
## Run 2 stress 0.1875618 
## ... Procrustes: rmse 0.003730648  max resid 0.02466595 
## Run 3 stress 0.2326598 
## Run 4 stress 0.1875618 
## ... Procrustes: rmse 0.003717748  max resid 0.02457644 
## Run 5 stress 0.1875527 
## ... Procrustes: rmse 0.01029553  max resid 0.07257547 
## Run 6 stress 0.1875527 
## ... Procrustes: rmse 0.01029144  max resid 0.07255269 
## Run 7 stress 0.1875527 
## ... Procrustes: rmse 0.01029292  max resid 0.07256231 
## Run 8 stress 0.2095598 
## Run 9 stress 0.2105465 
## Run 10 stress 0.1875527 
## ... Procrustes: rmse 0.0102898  max resid 0.07254486 
## Run 11 stress 0.2066865 
## Run 12 stress 0.2312508 
## Run 13 stress 0.1875625 
## ... Procrustes: rmse 0.003884934  max resid 0.02582226 
## Run 14 stress 0.1875527 
## ... Procrustes: rmse 0.01030238  max resid 0.07263194 
## Run 15 stress 0.1875527 
## ... Procrustes: rmse 0.01029361  max resid 0.07256713 
## Run 16 stress 0.1875527 
## ... Procrustes: rmse 0.01028975  max resid 0.0725293 
## Run 17 stress 0.1875618 
## ... Procrustes: rmse 0.003719725  max resid 0.02454185 
## Run 18 stress 0.2105466 
## Run 19 stress 0.2096271 
## Run 20 stress 0.2066864 
## *** No convergence -- monoMDS stopping criteria:
##     19: stress ratio > sratmax
##      1: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1821758 
## Run 1 stress 0.1879531 
## Run 2 stress 0.1877436 
## Run 3 stress 0.1877651 
## Run 4 stress 0.190829 
## Run 5 stress 0.1871566 
## Run 6 stress 0.1878673 
## Run 7 stress 0.196424 
## Run 8 stress 0.1871566 
## Run 9 stress 0.1997363 
## Run 10 stress 0.2106503 
## Run 11 stress 0.182137 
## ... New best solution
## ... Procrustes: rmse 0.005806067  max resid 0.04203009 
## Run 12 stress 0.1899351 
## Run 13 stress 0.2008168 
## Run 14 stress 0.1949076 
## Run 15 stress 0.1871502 
## Run 16 stress 0.1939492 
## Run 17 stress 0.182636 
## ... Procrustes: rmse 0.00971831  max resid 0.0550377 
## Run 18 stress 0.1879534 
## Run 19 stress 0.1899244 
## Run 20 stress 0.1915868 
## *** No convergence -- monoMDS stopping criteria:
##     19: stress ratio > sratmax
##      1: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1728594 
## Run 1 stress 0.1727911 
## ... New best solution
## ... Procrustes: rmse 0.006041499  max resid 0.03799394 
## Run 2 stress 0.1727719 
## ... New best solution
## ... Procrustes: rmse 0.002102114  max resid 0.0136238 
## Run 3 stress 0.1727697 
## ... New best solution
## ... Procrustes: rmse 0.0003959877  max resid 0.002702283 
## ... Similar to previous best
## Run 4 stress 0.1727699 
## ... Procrustes: rmse 5.972941e-05  max resid 0.0003625102 
## ... Similar to previous best
## Run 5 stress 0.1731677 
## ... Procrustes: rmse 0.008687875  max resid 0.0403693 
## Run 6 stress 0.1832575 
## Run 7 stress 0.1727694 
## ... New best solution
## ... Procrustes: rmse 0.000182532  max resid 0.001166911 
## ... Similar to previous best
## Run 8 stress 0.1728555 
## ... Procrustes: rmse 0.005962931  max resid 0.03793635 
## Run 9 stress 0.1731678 
## ... Procrustes: rmse 0.008627619  max resid 0.04013339 
## Run 10 stress 0.1832579 
## Run 11 stress 0.1727697 
## ... Procrustes: rmse 0.000162877  max resid 0.001067674 
## ... Similar to previous best
## Run 12 stress 0.1731678 
## ... Procrustes: rmse 0.008629405  max resid 0.04012422 
## Run 13 stress 0.1728597 
## ... Procrustes: rmse 0.006711308  max resid 0.03906967 
## Run 14 stress 0.1727697 
## ... Procrustes: rmse 0.0001688499  max resid 0.001102657 
## ... Similar to previous best
## Run 15 stress 0.1727741 
## ... Procrustes: rmse 0.0007430364  max resid 0.004973579 
## ... Similar to previous best
## Run 16 stress 0.172773 
## ... Procrustes: rmse 0.0007127333  max resid 0.004845445 
## ... Similar to previous best
## Run 17 stress 0.1728564 
## ... Procrustes: rmse 0.00593131  max resid 0.03790944 
## Run 18 stress 0.183258 
## Run 19 stress 0.1728594 
## ... Procrustes: rmse 0.006705524  max resid 0.03903445 
## Run 20 stress 0.1727694 
## ... Procrustes: rmse 5.037598e-05  max resid 0.0003046885 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1742136 
## Run 1 stress 0.1742393 
## ... Procrustes: rmse 0.002056202  max resid 0.01131298 
## Run 2 stress 0.1742426 
## ... Procrustes: rmse 0.002093411  max resid 0.01135176 
## Run 3 stress 0.1742434 
## ... Procrustes: rmse 0.002221983  max resid 0.01127869 
## Run 4 stress 0.1742153 
## ... Procrustes: rmse 0.002169998  max resid 0.01114556 
## Run 5 stress 0.2178045 
## Run 6 stress 0.2127924 
## Run 7 stress 0.1742318 
## ... Procrustes: rmse 0.001790808  max resid 0.01115193 
## Run 8 stress 0.2175262 
## Run 9 stress 0.2352813 
## Run 10 stress 0.2132001 
## Run 11 stress 0.1742384 
## ... Procrustes: rmse 0.002054161  max resid 0.01125592 
## Run 12 stress 0.1742206 
## ... Procrustes: rmse 0.0006144124  max resid 0.003465283 
## ... Similar to previous best
## Run 13 stress 0.1742303 
## ... Procrustes: rmse 0.001780432  max resid 0.01112403 
## Run 14 stress 0.1742857 
## ... Procrustes: rmse 0.004320328  max resid 0.02357573 
## Run 15 stress 0.1742399 
## ... Procrustes: rmse 0.002124847  max resid 0.01128626 
## Run 16 stress 0.17423 
## ... Procrustes: rmse 0.001776036  max resid 0.01111521 
## Run 17 stress 0.1742345 
## ... Procrustes: rmse 0.001885097  max resid 0.01118258 
## Run 18 stress 0.2149854 
## Run 19 stress 0.174545 
## ... Procrustes: rmse 0.007105394  max resid 0.04009053 
## Run 20 stress 0.2019257 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1864509 
## Run 1 stress 0.1866276 
## ... Procrustes: rmse 0.003944203  max resid 0.02499313 
## Run 2 stress 0.1967001 
## Run 3 stress 0.1871682 
## Run 4 stress 0.1866296 
## ... Procrustes: rmse 0.008930746  max resid 0.04334465 
## Run 5 stress 0.1876463 
## Run 6 stress 0.1872107 
## Run 7 stress 0.1965815 
## Run 8 stress 0.1865067 
## ... Procrustes: rmse 0.001841989  max resid 0.01072541 
## Run 9 stress 0.18663 
## ... Procrustes: rmse 0.009072128  max resid 0.04448871 
## Run 10 stress 0.1866296 
## ... Procrustes: rmse 0.008887181  max resid 0.0430039 
## Run 11 stress 0.1866296 
## ... Procrustes: rmse 0.00890705  max resid 0.04315848 
## Run 12 stress 0.1866299 
## ... Procrustes: rmse 0.00904365  max resid 0.04426748 
## Run 13 stress 0.1872109 
## Run 14 stress 0.186681 
## ... Procrustes: rmse 0.009235142  max resid 0.04419763 
## Run 15 stress 0.2334132 
## Run 16 stress 0.2541016 
## Run 17 stress 0.186884 
## ... Procrustes: rmse 0.009725193  max resid 0.04274832 
## Run 18 stress 0.1967021 
## Run 19 stress 0.1869915 
## Run 20 stress 0.1866296 
## ... Procrustes: rmse 0.008944563  max resid 0.04346556 
## *** No convergence -- monoMDS stopping criteria:
##      1: no. of iterations >= maxit
##     19: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1891473 
## Run 1 stress 0.4066248 
## Run 2 stress 0.1870536 
## ... New best solution
## ... Procrustes: rmse 0.02830164  max resid 0.169005 
## Run 3 stress 0.191121 
## Run 4 stress 0.1894983 
## Run 5 stress 0.1870538 
## ... Procrustes: rmse 0.0001845659  max resid 0.001202453 
## ... Similar to previous best
## Run 6 stress 0.1909159 
## Run 7 stress 0.2097651 
## Run 8 stress 0.1870539 
## ... Procrustes: rmse 7.659384e-05  max resid 0.000410041 
## ... Similar to previous best
## Run 9 stress 0.1870541 
## ... Procrustes: rmse 0.0003113738  max resid 0.002109818 
## ... Similar to previous best
## Run 10 stress 0.1909185 
## Run 11 stress 0.205467 
## Run 12 stress 0.1930387 
## Run 13 stress 0.1909159 
## Run 14 stress 0.2036172 
## Run 15 stress 0.2073884 
## Run 16 stress 0.1915624 
## Run 17 stress 0.1868665 
## ... New best solution
## ... Procrustes: rmse 0.007748254  max resid 0.04610815 
## Run 18 stress 0.1868664 
## ... New best solution
## ... Procrustes: rmse 4.753065e-05  max resid 0.0002095712 
## ... Similar to previous best
## Run 19 stress 0.1870541 
## ... Procrustes: rmse 0.007880155  max resid 0.04633346 
## Run 20 stress 0.1891004 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1770762 
## Run 1 stress 0.1770825 
## ... Procrustes: rmse 0.0008693537  max resid 0.003943071 
## ... Similar to previous best
## Run 2 stress 0.17977 
## Run 3 stress 0.1770812 
## ... Procrustes: rmse 0.0007404488  max resid 0.003901623 
## ... Similar to previous best
## Run 4 stress 0.1839565 
## Run 5 stress 0.1839564 
## Run 6 stress 0.1839564 
## Run 7 stress 0.1770822 
## ... Procrustes: rmse 0.0008474877  max resid 0.003938287 
## ... Similar to previous best
## Run 8 stress 0.1818929 
## Run 9 stress 0.1839564 
## Run 10 stress 0.1770762 
## ... New best solution
## ... Procrustes: rmse 3.198938e-05  max resid 0.0001415899 
## ... Similar to previous best
## Run 11 stress 0.177076 
## ... New best solution
## ... Procrustes: rmse 6.643889e-05  max resid 0.0002459714 
## ... Similar to previous best
## Run 12 stress 0.1770761 
## ... Procrustes: rmse 3.215675e-05  max resid 0.0001751725 
## ... Similar to previous best
## Run 13 stress 0.181769 
## Run 14 stress 0.177076 
## ... New best solution
## ... Procrustes: rmse 2.260129e-05  max resid 0.0001008824 
## ... Similar to previous best
## Run 15 stress 0.1770806 
## ... Procrustes: rmse 0.0006355951  max resid 0.003847123 
## ... Similar to previous best
## Run 16 stress 0.1770807 
## ... Procrustes: rmse 0.0006630747  max resid 0.003864112 
## ... Similar to previous best
## Run 17 stress 0.1797698 
## Run 18 stress 0.1839564 
## Run 19 stress 0.1839566 
## Run 20 stress 0.1770809 
## ... Procrustes: rmse 0.0006493665  max resid 0.003851454 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1782136 
## Run 1 stress 0.1784765 
## ... Procrustes: rmse 0.006084041  max resid 0.03697257 
## Run 2 stress 0.1782136 
## ... New best solution
## ... Procrustes: rmse 1.354728e-05  max resid 6.754975e-05 
## ... Similar to previous best
## Run 3 stress 0.1782313 
## ... Procrustes: rmse 0.003424529  max resid 0.02540403 
## Run 4 stress 0.1782103 
## ... New best solution
## ... Procrustes: rmse 0.0007471869  max resid 0.004407587 
## ... Similar to previous best
## Run 5 stress 0.1782103 
## ... Procrustes: rmse 0.0001272564  max resid 0.0008859291 
## ... Similar to previous best
## Run 6 stress 0.2234971 
## Run 7 stress 0.4066402 
## Run 8 stress 0.1782136 
## ... Procrustes: rmse 0.0007490621  max resid 0.004416154 
## ... Similar to previous best
## Run 9 stress 0.1782103 
## ... Procrustes: rmse 9.423713e-05  max resid 0.0006417563 
## ... Similar to previous best
## Run 10 stress 0.1782105 
## ... Procrustes: rmse 0.0001340003  max resid 0.000896655 
## ... Similar to previous best
## Run 11 stress 0.1784774 
## ... Procrustes: rmse 0.005999608  max resid 0.03669724 
## Run 12 stress 0.1813525 
## Run 13 stress 0.1782103 
## ... Procrustes: rmse 7.825216e-05  max resid 0.0005463202 
## ... Similar to previous best
## Run 14 stress 0.1782103 
## ... Procrustes: rmse 0.000102705  max resid 0.0007174098 
## ... Similar to previous best
## Run 15 stress 0.1782136 
## ... Procrustes: rmse 0.0007491371  max resid 0.004412754 
## ... Similar to previous best
## Run 16 stress 0.1782282 
## ... Procrustes: rmse 0.003416444  max resid 0.02535108 
## Run 17 stress 0.1784768 
## ... Procrustes: rmse 0.006240043  max resid 0.03728032 
## Run 18 stress 0.1782136 
## ... Procrustes: rmse 0.0007472772  max resid 0.004408359 
## ... Similar to previous best
## Run 19 stress 0.1784768 
## ... Procrustes: rmse 0.006240445  max resid 0.037284 
## Run 20 stress 0.1782137 
## ... Procrustes: rmse 0.0007594819  max resid 0.004414149 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1779773 
## Run 1 stress 0.1781438 
## ... Procrustes: rmse 0.01074618  max resid 0.0748357 
## Run 2 stress 0.1972246 
## Run 3 stress 0.1779772 
## ... New best solution
## ... Procrustes: rmse 0.0002839653  max resid 0.001521159 
## ... Similar to previous best
## Run 4 stress 0.2091888 
## Run 5 stress 0.1781434 
## ... Procrustes: rmse 0.01045016  max resid 0.07399386 
## Run 6 stress 0.1781435 
## ... Procrustes: rmse 0.01060859  max resid 0.07467526 
## Run 7 stress 0.1819159 
## Run 8 stress 0.1779216 
## ... New best solution
## ... Procrustes: rmse 0.004928058  max resid 0.03036705 
## Run 9 stress 0.17972 
## Run 10 stress 0.2092 
## Run 11 stress 0.1797221 
## Run 12 stress 0.1808562 
## Run 13 stress 0.1808562 
## Run 14 stress 0.178147 
## ... Procrustes: rmse 0.01392132  max resid 0.104108 
## Run 15 stress 0.1797193 
## Run 16 stress 0.2263344 
## Run 17 stress 0.1808584 
## Run 18 stress 0.1819326 
## Run 19 stress 0.1908401 
## Run 20 stress 0.180857 
## *** No convergence -- monoMDS stopping criteria:
##     20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.2141035 
## Run 1 stress 0.2173049 
## Run 2 stress 0.2130141 
## ... New best solution
## ... Procrustes: rmse 0.03280388  max resid 0.1798519 
## Run 3 stress 0.2144367 
## Run 4 stress 0.2290151 
## Run 5 stress 0.2130785 
## ... Procrustes: rmse 0.005693901  max resid 0.0361183 
## Run 6 stress 0.2157648 
## Run 7 stress 0.2274414 
## Run 8 stress 0.2183311 
## Run 9 stress 0.2130153 
## ... Procrustes: rmse 0.0005059794  max resid 0.003176342 
## ... Similar to previous best
## Run 10 stress 0.2130169 
## ... Procrustes: rmse 0.0007227888  max resid 0.004301562 
## ... Similar to previous best
## Run 11 stress 0.2130178 
## ... Procrustes: rmse 0.0008817058  max resid 0.005768768 
## ... Similar to previous best
## Run 12 stress 0.2224566 
## Run 13 stress 0.2290861 
## Run 14 stress 0.2316146 
## Run 15 stress 0.2178871 
## Run 16 stress 0.2301753 
## Run 17 stress 0.2487429 
## Run 18 stress 0.2145932 
## Run 19 stress 0.2185976 
## Run 20 stress 0.2290861 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1950622 
## Run 1 stress 0.4072655 
## Run 2 stress 0.1964355 
## Run 3 stress 0.19505 
## ... New best solution
## ... Procrustes: rmse 0.02041892  max resid 0.1523433 
## Run 4 stress 0.203728 
## Run 5 stress 0.2093407 
## Run 6 stress 0.1950622 
## ... Procrustes: rmse 0.02047519  max resid 0.1527665 
## Run 7 stress 0.1971281 
## Run 8 stress 0.1950501 
## ... Procrustes: rmse 9.963248e-05  max resid 0.0006720585 
## ... Similar to previous best
## Run 9 stress 0.1964738 
## Run 10 stress 0.2238816 
## Run 11 stress 0.19505 
## ... Procrustes: rmse 1.307048e-05  max resid 6.094718e-05 
## ... Similar to previous best
## Run 12 stress 0.1964353 
## Run 13 stress 0.1970423 
## Run 14 stress 0.1964743 
## Run 15 stress 0.2037287 
## Run 16 stress 0.1971294 
## Run 17 stress 0.19505 
## ... Procrustes: rmse 1.925538e-05  max resid 0.0001062048 
## ... Similar to previous best
## Run 18 stress 0.2093301 
## Run 19 stress 0.197046 
## Run 20 stress 0.2150376 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.197 
## Run 1 stress 0.1976006 
## Run 2 stress 0.2040656 
## Run 3 stress 0.1970012 
## ... Procrustes: rmse 0.0002339557  max resid 0.001117705 
## ... Similar to previous best
## Run 4 stress 0.2181836 
## Run 5 stress 0.1976408 
## Run 6 stress 0.2024077 
## Run 7 stress 0.2042805 
## Run 8 stress 0.1977643 
## Run 9 stress 0.1979196 
## Run 10 stress 0.1977643 
## Run 11 stress 0.1979197 
## Run 12 stress 0.1986713 
## Run 13 stress 0.2151953 
## Run 14 stress 0.2025296 
## Run 15 stress 0.1977647 
## Run 16 stress 0.2173611 
## Run 17 stress 0.1986427 
## Run 18 stress 0.2051211 
## Run 19 stress 0.1975449 
## Run 20 stress 0.2046347 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1935637 
## Run 1 stress 0.1935442 
## ... New best solution
## ... Procrustes: rmse 0.001799763  max resid 0.01041083 
## Run 2 stress 0.1924876 
## ... New best solution
## ... Procrustes: rmse 0.03160737  max resid 0.131905 
## Run 3 stress 0.1935625 
## Run 4 stress 0.1967101 
## Run 5 stress 0.1958003 
## Run 6 stress 0.1961546 
## Run 7 stress 0.1935643 
## Run 8 stress 0.1960476 
## Run 9 stress 0.1942672 
## Run 10 stress 0.1967443 
## Run 11 stress 0.2378625 
## Run 12 stress 0.1925342 
## ... Procrustes: rmse 0.02800754  max resid 0.1284411 
## Run 13 stress 0.1965406 
## Run 14 stress 0.1957997 
## Run 15 stress 0.1960145 
## Run 16 stress 0.1960143 
## Run 17 stress 0.1935443 
## Run 18 stress 0.201235 
## Run 19 stress 0.1983769 
## Run 20 stress 0.2012492 
## *** No convergence -- monoMDS stopping criteria:
##     20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1824375 
## Run 1 stress 0.1824375 
## ... New best solution
## ... Procrustes: rmse 1.183988e-05  max resid 7.819541e-05 
## ... Similar to previous best
## Run 2 stress 0.1799002 
## ... New best solution
## ... Procrustes: rmse 0.03638419  max resid 0.2833504 
## Run 3 stress 0.1802371 
## ... Procrustes: rmse 0.01568607  max resid 0.1187144 
## Run 4 stress 0.1824375 
## Run 5 stress 0.1799164 
## ... Procrustes: rmse 0.001152904  max resid 0.006458535 
## ... Similar to previous best
## Run 6 stress 0.1798997 
## ... New best solution
## ... Procrustes: rmse 0.000924637  max resid 0.005496584 
## ... Similar to previous best
## Run 7 stress 0.1802375 
## ... Procrustes: rmse 0.01591901  max resid 0.1203792 
## Run 8 stress 0.180238 
## ... Procrustes: rmse 0.01559536  max resid 0.117611 
## Run 9 stress 0.1799065 
## ... Procrustes: rmse 0.001087964  max resid 0.005780038 
## ... Similar to previous best
## Run 10 stress 0.1827093 
## Run 11 stress 0.1799 
## ... Procrustes: rmse 7.934643e-05  max resid 0.0004375639 
## ... Similar to previous best
## Run 12 stress 0.1824375 
## Run 13 stress 0.1798999 
## ... Procrustes: rmse 7.35966e-05  max resid 0.0004380104 
## ... Similar to previous best
## Run 14 stress 0.180237 
## ... Procrustes: rmse 0.0158574  max resid 0.1197689 
## Run 15 stress 0.182784 
## Run 16 stress 0.1799163 
## ... Procrustes: rmse 0.001755132  max resid 0.007146625 
## ... Similar to previous best
## Run 17 stress 0.1799134 
## ... Procrustes: rmse 0.001493537  max resid 0.006323934 
## ... Similar to previous best
## Run 18 stress 0.1798996 
## ... New best solution
## ... Procrustes: rmse 0.0008734725  max resid 0.005340798 
## ... Similar to previous best
## Run 19 stress 0.182784 
## Run 20 stress 0.1799 
## ... Procrustes: rmse 0.0007796546  max resid 0.004751483 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1945802 
## Run 1 stress 0.2021536 
## Run 2 stress 0.2004611 
## Run 3 stress 0.194604 
## ... Procrustes: rmse 0.01156539  max resid 0.04097248 
## Run 4 stress 0.1947028 
## ... Procrustes: rmse 0.00769767  max resid 0.03726731 
## Run 5 stress 0.2004504 
## Run 6 stress 0.2021535 
## Run 7 stress 0.1945791 
## ... New best solution
## ... Procrustes: rmse 0.008331195  max resid 0.03837592 
## Run 8 stress 0.2090408 
## Run 9 stress 0.2215714 
## Run 10 stress 0.1947029 
## ... Procrustes: rmse 0.00988  max resid 0.03513249 
## Run 11 stress 0.2019956 
## Run 12 stress 0.1946038 
## ... Procrustes: rmse 0.006979456  max resid 0.0364319 
## Run 13 stress 0.1946664 
## ... Procrustes: rmse 0.005119146  max resid 0.03556831 
## Run 14 stress 0.1948184 
## ... Procrustes: rmse 0.01456816  max resid 0.09094829 
## Run 15 stress 0.2195094 
## Run 16 stress 0.1946657 
## ... Procrustes: rmse 0.0150406  max resid 0.09210628 
## Run 17 stress 0.223662 
## Run 18 stress 0.2125449 
## Run 19 stress 0.1944898 
## ... New best solution
## ... Procrustes: rmse 0.00684143  max resid 0.03219302 
## Run 20 stress 0.1946038 
## ... Procrustes: rmse 0.007601894  max resid 0.03902079 
## *** No convergence -- monoMDS stopping criteria:
##     20: stress ratio > sratmax
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1905614 
## Run 1 stress 0.1959151 
## Run 2 stress 0.2171768 
## Run 3 stress 0.2242984 
## Run 4 stress 0.1959211 
## Run 5 stress 0.2271224 
## Run 6 stress 0.1920407 
## Run 7 stress 0.1905913 
## ... Procrustes: rmse 0.0027797  max resid 0.01887006 
## Run 8 stress 0.1905595 
## ... New best solution
## ... Procrustes: rmse 0.004425766  max resid 0.02283778 
## Run 9 stress 0.192044 
## Run 10 stress 0.1959157 
## Run 11 stress 0.1920442 
## Run 12 stress 0.2254135 
## Run 13 stress 0.1903248 
## ... New best solution
## ... Procrustes: rmse 0.007841821  max resid 0.04473863 
## Run 14 stress 0.1903248 
## ... Procrustes: rmse 4.338024e-05  max resid 0.0002875893 
## ... Similar to previous best
## Run 15 stress 0.2153495 
## Run 16 stress 0.1920431 
## Run 17 stress 0.1920456 
## Run 18 stress 0.229066 
## Run 19 stress 0.2165586 
## Run 20 stress 0.1959181 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.2063212 
## Run 1 stress 0.2090702 
## Run 2 stress 0.2080069 
## Run 3 stress 0.2090699 
## Run 4 stress 0.2488213 
## Run 5 stress 0.2090611 
## Run 6 stress 0.2063188 
## ... New best solution
## ... Procrustes: rmse 0.0004045549  max resid 0.001698455 
## ... Similar to previous best
## Run 7 stress 0.2534538 
## Run 8 stress 0.2080069 
## Run 9 stress 0.2090698 
## Run 10 stress 0.236734 
## Run 11 stress 0.4077266 
## Run 12 stress 0.2090699 
## Run 13 stress 0.2083877 
## Run 14 stress 0.2090699 
## Run 15 stress 0.20907 
## Run 16 stress 0.212576 
## Run 17 stress 0.2083428 
## Run 18 stress 0.2063195 
## ... Procrustes: rmse 0.0002972807  max resid 0.001275668 
## ... Similar to previous best
## Run 19 stress 0.2090698 
## Run 20 stress 0.2083444 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0762502 
## Run 1 stress 0.07625021 
## ... Procrustes: rmse 1.366488e-05  max resid 7.766714e-05 
## ... Similar to previous best
## Run 2 stress 0.08614381 
## Run 3 stress 0.07130037 
## ... New best solution
## ... Procrustes: rmse 0.03267107  max resid 0.2604145 
## Run 4 stress 0.0762502 
## Run 5 stress 0.1132713 
## Run 6 stress 0.1046431 
## Run 7 stress 0.08193687 
## Run 8 stress 0.08619594 
## Run 9 stress 0.08614369 
## Run 10 stress 0.1324131 
## Run 11 stress 0.0861957 
## Run 12 stress 0.0762503 
## Run 13 stress 0.07625028 
## Run 14 stress 0.12416 
## Run 15 stress 0.08193689 
## Run 16 stress 0.07625021 
## Run 17 stress 0.08194626 
## Run 18 stress 0.0762502 
## Run 19 stress 0.08619573 
## Run 20 stress 0.0762502 
## *** No convergence -- monoMDS stopping criteria:
##     17: stress ratio > sratmax
##      3: scale factor of the gradient < sfgrmin
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08481971 
## Run 1 stress 0.08482014 
## ... Procrustes: rmse 0.001897914  max resid 0.01270675 
## Run 2 stress 0.08481768 
## ... New best solution
## ... Procrustes: rmse 0.0002494052  max resid 0.001559841 
## ... Similar to previous best
## Run 3 stress 0.08482271 
## ... Procrustes: rmse 0.0005148402  max resid 0.003243802 
## ... Similar to previous best
## Run 4 stress 0.08481903 
## ... Procrustes: rmse 0.00151954  max resid 0.01026913 
## Run 5 stress 0.084822 
## ... Procrustes: rmse 0.0003808411  max resid 0.002010741 
## ... Similar to previous best
## Run 6 stress 0.08481975 
## ... Procrustes: rmse 0.0002191837  max resid 0.001331836 
## ... Similar to previous best
## Run 7 stress 0.08481655 
## ... New best solution
## ... Procrustes: rmse 0.001201592  max resid 0.008103075 
## ... Similar to previous best
## Run 8 stress 0.08481897 
## ... Procrustes: rmse 0.001330943  max resid 0.008982136 
## ... Similar to previous best
## Run 9 stress 0.0848221 
## ... Procrustes: rmse 0.0006232144  max resid 0.004216975 
## ... Similar to previous best
## Run 10 stress 0.08481864 
## ... Procrustes: rmse 0.001342561  max resid 0.008996008 
## ... Similar to previous best
## Run 11 stress 0.08481786 
## ... Procrustes: rmse 0.0008374444  max resid 0.004469169 
## ... Similar to previous best
## Run 12 stress 0.08482044 
## ... Procrustes: rmse 0.001536888  max resid 0.01024284 
## Run 13 stress 0.08481867 
## ... Procrustes: rmse 0.001358826  max resid 0.009027846 
## ... Similar to previous best
## Run 14 stress 0.08481631 
## ... New best solution
## ... Procrustes: rmse 0.0008047481  max resid 0.004316925 
## ... Similar to previous best
## Run 15 stress 0.08481928 
## ... Procrustes: rmse 0.0007265349  max resid 0.005143873 
## ... Similar to previous best
## Run 16 stress 0.08482282 
## ... Procrustes: rmse 0.001448681  max resid 0.009072121 
## ... Similar to previous best
## Run 17 stress 0.08482621 
## ... Procrustes: rmse 0.001604087  max resid 0.009898067 
## ... Similar to previous best
## Run 18 stress 0.08482233 
## ... Procrustes: rmse 0.0008876703  max resid 0.006285566 
## ... Similar to previous best
## Run 19 stress 0.08481895 
## ... Procrustes: rmse 0.001106423  max resid 0.006547255 
## ... Similar to previous best
## Run 20 stress 0.08481606 
## ... New best solution
## ... Procrustes: rmse 0.0007222563  max resid 0.003686685 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0835775 
## Run 1 stress 0.08357751 
## ... Procrustes: rmse 3.081082e-05  max resid 0.0001271349 
## ... Similar to previous best
## Run 2 stress 0.08357766 
## ... Procrustes: rmse 9.659152e-05  max resid 0.0005146427 
## ... Similar to previous best
## Run 3 stress 0.0835775 
## ... New best solution
## ... Procrustes: rmse 1.955098e-05  max resid 7.635037e-05 
## ... Similar to previous best
## Run 4 stress 0.08357754 
## ... Procrustes: rmse 3.850813e-05  max resid 0.0002230852 
## ... Similar to previous best
## Run 5 stress 0.08357751 
## ... Procrustes: rmse 3.373048e-05  max resid 0.0001454563 
## ... Similar to previous best
## Run 6 stress 0.08357762 
## ... Procrustes: rmse 2.46504e-05  max resid 0.0001157568 
## ... Similar to previous best
## Run 7 stress 0.08357753 
## ... Procrustes: rmse 3.541417e-05  max resid 0.0002424505 
## ... Similar to previous best
## Run 8 stress 0.08357754 
## ... Procrustes: rmse 5.146239e-05  max resid 0.0002249132 
## ... Similar to previous best
## Run 9 stress 0.08357752 
## ... Procrustes: rmse 2.696773e-05  max resid 0.0001761893 
## ... Similar to previous best
## Run 10 stress 0.0835775 
## ... New best solution
## ... Procrustes: rmse 8.74367e-06  max resid 4.559658e-05 
## ... Similar to previous best
## Run 11 stress 0.0835775 
## ... Procrustes: rmse 1.661321e-05  max resid 7.599255e-05 
## ... Similar to previous best
## Run 12 stress 0.08357772 
## ... Procrustes: rmse 0.0001061425  max resid 0.000466474 
## ... Similar to previous best
## Run 13 stress 0.0835775 
## ... New best solution
## ... Procrustes: rmse 6.156195e-06  max resid 3.971743e-05 
## ... Similar to previous best
## Run 14 stress 0.0835775 
## ... Procrustes: rmse 2.189526e-05  max resid 9.64143e-05 
## ... Similar to previous best
## Run 15 stress 0.0835775 
## ... Procrustes: rmse 1.618422e-05  max resid 9.460451e-05 
## ... Similar to previous best
## Run 16 stress 0.0835775 
## ... Procrustes: rmse 7.934605e-06  max resid 2.559633e-05 
## ... Similar to previous best
## Run 17 stress 0.0835775 
## ... Procrustes: rmse 9.436833e-06  max resid 4.275371e-05 
## ... Similar to previous best
## Run 18 stress 0.08357762 
## ... Procrustes: rmse 3.708843e-05  max resid 0.0001408645 
## ... Similar to previous best
## Run 19 stress 0.0835775 
## ... Procrustes: rmse 8.050846e-06  max resid 2.949371e-05 
## ... Similar to previous best
## Run 20 stress 0.0835775 
## ... Procrustes: rmse 1.027368e-05  max resid 4.33024e-05 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09932353 
## Run 1 stress 0.0984318 
## ... New best solution
## ... Procrustes: rmse 0.0104003  max resid 0.05777218 
## Run 2 stress 0.09843014 
## ... New best solution
## ... Procrustes: rmse 0.0002115517  max resid 0.0008317289 
## ... Similar to previous best
## Run 3 stress 0.09593944 
## ... New best solution
## ... Procrustes: rmse 0.03044474  max resid 0.154073 
## Run 4 stress 0.09594304 
## ... Procrustes: rmse 0.0007449018  max resid 0.004894359 
## ... Similar to previous best
## Run 5 stress 0.09594093 
## ... Procrustes: rmse 0.000596224  max resid 0.003853818 
## ... Similar to previous best
## Run 6 stress 0.09843232 
## Run 7 stress 0.09843301 
## Run 8 stress 0.09593959 
## ... Procrustes: rmse 3.672048e-05  max resid 0.000144838 
## ... Similar to previous best
## Run 9 stress 0.09843251 
## Run 10 stress 0.0959394 
## ... New best solution
## ... Procrustes: rmse 0.0003317936  max resid 0.001965994 
## ... Similar to previous best
## Run 11 stress 0.09843166 
## Run 12 stress 0.09593932 
## ... New best solution
## ... Procrustes: rmse 0.0002921705  max resid 0.001753039 
## ... Similar to previous best
## Run 13 stress 0.09932279 
## Run 14 stress 0.09843134 
## Run 15 stress 0.09843174 
## Run 16 stress 0.09594036 
## ... Procrustes: rmse 0.0004858126  max resid 0.003135034 
## ... Similar to previous best
## Run 17 stress 0.09843023 
## Run 18 stress 0.09593958 
## ... Procrustes: rmse 0.0003468084  max resid 0.002170641 
## ... Similar to previous best
## Run 19 stress 0.09932407 
## Run 20 stress 0.09593933 
## ... Procrustes: rmse 1.132793e-05  max resid 3.7321e-05 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1066799 
## Run 1 stress 0.1076751 
## Run 2 stress 0.1076784 
## Run 3 stress 0.1076765 
## Run 4 stress 0.1057466 
## ... New best solution
## ... Procrustes: rmse 0.02311791  max resid 0.1215968 
## Run 5 stress 0.1076743 
## Run 6 stress 0.1057477 
## ... Procrustes: rmse 0.0001968286  max resid 0.0006912121 
## ... Similar to previous best
## Run 7 stress 0.1057467 
## ... Procrustes: rmse 5.600574e-05  max resid 0.0003069181 
## ... Similar to previous best
## Run 8 stress 0.1057461 
## ... New best solution
## ... Procrustes: rmse 0.0001077062  max resid 0.0003066837 
## ... Similar to previous best
## Run 9 stress 0.1057468 
## ... Procrustes: rmse 0.0003543134  max resid 0.001096729 
## ... Similar to previous best
## Run 10 stress 0.1057465 
## ... Procrustes: rmse 8.409558e-05  max resid 0.0002488517 
## ... Similar to previous best
## Run 11 stress 0.1060363 
## ... Procrustes: rmse 0.03599433  max resid 0.1347833 
## Run 12 stress 0.1060371 
## ... Procrustes: rmse 0.03590769  max resid 0.1347016 
## Run 13 stress 0.1076763 
## Run 14 stress 0.1060351 
## ... Procrustes: rmse 0.03620896  max resid 0.1349582 
## Run 15 stress 0.1057481 
## ... Procrustes: rmse 0.0002856175  max resid 0.000921147 
## ... Similar to previous best
## Run 16 stress 0.1057477 
## ... Procrustes: rmse 0.0002413474  max resid 0.0007939904 
## ... Similar to previous best
## Run 17 stress 0.1057483 
## ... Procrustes: rmse 0.0003660193  max resid 0.001261328 
## ... Similar to previous best
## Run 18 stress 0.1076766 
## Run 19 stress 0.1057466 
## ... Procrustes: rmse 0.0003599134  max resid 0.001080599 
## ... Similar to previous best
## Run 20 stress 0.1057488 
## ... Procrustes: rmse 0.0004035886  max resid 0.001400508 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08190885 
## Run 1 stress 0.08212793 
## ... Procrustes: rmse 0.006507115  max resid 0.0406766 
## Run 2 stress 0.08213592 
## ... Procrustes: rmse 0.007034557  max resid 0.04393245 
## Run 3 stress 0.08212813 
## ... Procrustes: rmse 0.0065163  max resid 0.04073186 
## Run 4 stress 0.08443189 
## Run 5 stress 0.08443199 
## Run 6 stress 0.08212678 
## ... Procrustes: rmse 0.006390256  max resid 0.03993689 
## Run 7 stress 0.08212031 
## ... Procrustes: rmse 0.005956041  max resid 0.0372044 
## Run 8 stress 0.08212467 
## ... Procrustes: rmse 0.006260704  max resid 0.03912373 
## Run 9 stress 0.08190889 
## ... Procrustes: rmse 3.582204e-05  max resid 0.0001726637 
## ... Similar to previous best
## Run 10 stress 0.08190883 
## ... New best solution
## ... Procrustes: rmse 4.713726e-05  max resid 0.0002205685 
## ... Similar to previous best
## Run 11 stress 0.08213004 
## ... Procrustes: rmse 0.006685334  max resid 0.04183871 
## Run 12 stress 0.08212974 
## ... Procrustes: rmse 0.006663342  max resid 0.04170315 
## Run 13 stress 0.08213359 
## ... Procrustes: rmse 0.006937145  max resid 0.04339651 
## Run 14 stress 0.08190914 
## ... Procrustes: rmse 4.347432e-05  max resid 0.0001620763 
## ... Similar to previous best
## Run 15 stress 0.08190989 
## ... Procrustes: rmse 0.0002108423  max resid 0.001148117 
## ... Similar to previous best
## Run 16 stress 0.08212624 
## ... Procrustes: rmse 0.006363967  max resid 0.0398307 
## Run 17 stress 0.08190933 
## ... Procrustes: rmse 4.560874e-05  max resid 0.0002599741 
## ... Similar to previous best
## Run 18 stress 0.08190905 
## ... Procrustes: rmse 5.001966e-05  max resid 0.000252484 
## ... Similar to previous best
## Run 19 stress 0.08443233 
## Run 20 stress 0.0844317 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0961181 
## Run 1 stress 0.09611728 
## ... New best solution
## ... Procrustes: rmse 0.001534403  max resid 0.006311335 
## ... Similar to previous best
## Run 2 stress 0.09611549 
## ... New best solution
## ... Procrustes: rmse 0.001216234  max resid 0.004967387 
## ... Similar to previous best
## Run 3 stress 0.09611499 
## ... New best solution
## ... Procrustes: rmse 0.0009164347  max resid 0.003781783 
## ... Similar to previous best
## Run 4 stress 0.09611617 
## ... Procrustes: rmse 0.001011884  max resid 0.004204722 
## ... Similar to previous best
## Run 5 stress 0.09611717 
## ... Procrustes: rmse 0.0002256515  max resid 0.0009568474 
## ... Similar to previous best
## Run 6 stress 0.09611551 
## ... Procrustes: rmse 7.634253e-05  max resid 0.0003212926 
## ... Similar to previous best
## Run 7 stress 0.09611751 
## ... Procrustes: rmse 0.001174544  max resid 0.004896106 
## ... Similar to previous best
## Run 8 stress 0.0961183 
## ... Procrustes: rmse 0.001260562  max resid 0.005267722 
## ... Similar to previous best
## Run 9 stress 0.09611496 
## ... New best solution
## ... Procrustes: rmse 7.796375e-05  max resid 0.0004770842 
## ... Similar to previous best
## Run 10 stress 0.09611428 
## ... New best solution
## ... Procrustes: rmse 0.0001604013  max resid 0.0009040269 
## ... Similar to previous best
## Run 11 stress 0.0961179 
## ... Procrustes: rmse 0.001059152  max resid 0.004456681 
## ... Similar to previous best
## Run 12 stress 0.09611527 
## ... Procrustes: rmse 0.0002105909  max resid 0.0008668645 
## ... Similar to previous best
## Run 13 stress 0.09611797 
## ... Procrustes: rmse 0.000534314  max resid 0.002233256 
## ... Similar to previous best
## Run 14 stress 0.09611832 
## ... Procrustes: rmse 0.001098526  max resid 0.004628895 
## ... Similar to previous best
## Run 15 stress 0.0961167 
## ... Procrustes: rmse 0.0009199504  max resid 0.003853301 
## ... Similar to previous best
## Run 16 stress 0.09611573 
## ... Procrustes: rmse 0.0002810339  max resid 0.001281665 
## ... Similar to previous best
## Run 17 stress 0.09611734 
## ... Procrustes: rmse 0.0004611139  max resid 0.001893511 
## ... Similar to previous best
## Run 18 stress 0.09611746 
## ... Procrustes: rmse 0.001012763  max resid 0.004259981 
## ... Similar to previous best
## Run 19 stress 0.09611485 
## ... Procrustes: rmse 0.0001204216  max resid 0.0004839872 
## ... Similar to previous best
## Run 20 stress 0.09611546 
## ... Procrustes: rmse 0.0007645561  max resid 0.003193129 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1099301 
## Run 1 stress 0.1099318 
## ... Procrustes: rmse 0.0004140296  max resid 0.001545275 
## ... Similar to previous best
## Run 2 stress 0.1179469 
## Run 3 stress 0.1099305 
## ... Procrustes: rmse 0.0002158247  max resid 0.0007781786 
## ... Similar to previous best
## Run 4 stress 0.1099299 
## ... New best solution
## ... Procrustes: rmse 8.969293e-05  max resid 0.0004285709 
## ... Similar to previous best
## Run 5 stress 0.1099308 
## ... Procrustes: rmse 0.0002483831  max resid 0.0009234473 
## ... Similar to previous best
## Run 6 stress 0.1099301 
## ... Procrustes: rmse 9.425112e-05  max resid 0.0004745901 
## ... Similar to previous best
## Run 7 stress 0.1099303 
## ... Procrustes: rmse 0.0002736489  max resid 0.001153758 
## ... Similar to previous best
## Run 8 stress 0.1099307 
## ... Procrustes: rmse 7.847177e-05  max resid 0.0002777343 
## ... Similar to previous best
## Run 9 stress 0.109931 
## ... Procrustes: rmse 0.0004076753  max resid 0.001760855 
## ... Similar to previous best
## Run 10 stress 0.1179496 
## Run 11 stress 0.1099305 
## ... Procrustes: rmse 0.0001876644  max resid 0.0006926543 
## ... Similar to previous best
## Run 12 stress 0.1099308 
## ... Procrustes: rmse 0.0003645297  max resid 0.001521797 
## ... Similar to previous best
## Run 13 stress 0.1179471 
## Run 14 stress 0.10993 
## ... Procrustes: rmse 0.000136739  max resid 0.0006121061 
## ... Similar to previous best
## Run 15 stress 0.1099303 
## ... Procrustes: rmse 0.000257145  max resid 0.001115565 
## ... Similar to previous best
## Run 16 stress 0.1099301 
## ... Procrustes: rmse 0.0001956494  max resid 0.0008507498 
## ... Similar to previous best
## Run 17 stress 0.1099299 
## ... New best solution
## ... Procrustes: rmse 3.16826e-05  max resid 0.0001332008 
## ... Similar to previous best
## Run 18 stress 0.1099308 
## ... Procrustes: rmse 0.0003280453  max resid 0.001400137 
## ... Similar to previous best
## Run 19 stress 0.1099305 
## ... Procrustes: rmse 0.0002551527  max resid 0.001067019 
## ... Similar to previous best
## Run 20 stress 0.1179503 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08381648 
## Run 1 stress 0.0832827 
## ... New best solution
## ... Procrustes: rmse 0.01423435  max resid 0.1035322 
## Run 2 stress 0.08328312 
## ... Procrustes: rmse 0.0001023973  max resid 0.0006241897 
## ... Similar to previous best
## Run 3 stress 0.0832831 
## ... Procrustes: rmse 9.675853e-05  max resid 0.0005890718 
## ... Similar to previous best
## Run 4 stress 0.08328377 
## ... Procrustes: rmse 0.0001810744  max resid 0.001097136 
## ... Similar to previous best
## Run 5 stress 0.08328342 
## ... Procrustes: rmse 0.0001243485  max resid 0.0007533637 
## ... Similar to previous best
## Run 6 stress 0.08381248 
## Run 7 stress 0.08328257 
## ... New best solution
## ... Procrustes: rmse 9.449508e-05  max resid 0.0004942327 
## ... Similar to previous best
## Run 8 stress 0.08328388 
## ... Procrustes: rmse 0.000292619  max resid 0.001702178 
## ... Similar to previous best
## Run 9 stress 0.08328361 
## ... Procrustes: rmse 0.0002643208  max resid 0.001545761 
## ... Similar to previous best
## Run 10 stress 0.08328258 
## ... Procrustes: rmse 2.456389e-05  max resid 0.0001168447 
## ... Similar to previous best
## Run 11 stress 0.08328319 
## ... Procrustes: rmse 0.0001716743  max resid 0.0009780238 
## ... Similar to previous best
## Run 12 stress 0.1050654 
## Run 13 stress 0.08328325 
## ... Procrustes: rmse 0.0002159286  max resid 0.001242848 
## ... Similar to previous best
## Run 14 stress 0.08381515 
## Run 15 stress 0.0832827 
## ... Procrustes: rmse 9.488326e-05  max resid 0.0005452454 
## ... Similar to previous best
## Run 16 stress 0.08381612 
## Run 17 stress 0.1050621 
## Run 18 stress 0.105063 
## Run 19 stress 0.0838151 
## Run 20 stress 0.083818 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1041644 
## Run 1 stress 0.1041625 
## ... New best solution
## ... Procrustes: rmse 0.0003037359  max resid 0.001473392 
## ... Similar to previous best
## Run 2 stress 0.1040527 
## ... New best solution
## ... Procrustes: rmse 0.005984428  max resid 0.03760406 
## Run 3 stress 0.1110082 
## Run 4 stress 0.1041626 
## ... Procrustes: rmse 0.005998679  max resid 0.03767646 
## Run 5 stress 0.1040521 
## ... New best solution
## ... Procrustes: rmse 9.760811e-05  max resid 0.0004987654 
## ... Similar to previous best
## Run 6 stress 0.1033648 
## ... New best solution
## ... Procrustes: rmse 0.0119179  max resid 0.08390788 
## Run 7 stress 0.1110063 
## Run 8 stress 0.1033648 
## ... New best solution
## ... Procrustes: rmse 3.915977e-05  max resid 0.0001323147 
## ... Similar to previous best
## Run 9 stress 0.1033647 
## ... New best solution
## ... Procrustes: rmse 5.16793e-05  max resid 0.0002119283 
## ... Similar to previous best
## Run 10 stress 0.1033653 
## ... Procrustes: rmse 0.000210657  max resid 0.0008244959 
## ... Similar to previous best
## Run 11 stress 0.1110072 
## Run 12 stress 0.1116054 
## Run 13 stress 0.103365 
## ... Procrustes: rmse 0.0001334103  max resid 0.0006515753 
## ... Similar to previous best
## Run 14 stress 0.1033648 
## ... Procrustes: rmse 5.359865e-05  max resid 0.0002164096 
## ... Similar to previous best
## Run 15 stress 0.1033656 
## ... Procrustes: rmse 0.0002553542  max resid 0.001060428 
## ... Similar to previous best
## Run 16 stress 0.1033657 
## ... Procrustes: rmse 0.0002758165  max resid 0.001159428 
## ... Similar to previous best
## Run 17 stress 0.1110065 
## Run 18 stress 0.1033651 
## ... Procrustes: rmse 0.0001752628  max resid 0.0006173408 
## ... Similar to previous best
## Run 19 stress 0.1033647 
## ... Procrustes: rmse 2.565979e-05  max resid 0.0001128623 
## ... Similar to previous best
## Run 20 stress 0.1041625 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08877039 
## Run 1 stress 0.08877039 
## ... New best solution
## ... Procrustes: rmse 1.230745e-05  max resid 5.641623e-05 
## ... Similar to previous best
## Run 2 stress 0.08877042 
## ... Procrustes: rmse 3.2707e-05  max resid 0.0001890862 
## ... Similar to previous best
## Run 3 stress 0.08877059 
## ... Procrustes: rmse 0.000100396  max resid 0.0007076914 
## ... Similar to previous best
## Run 4 stress 0.08877042 
## ... Procrustes: rmse 2.148744e-05  max resid 6.451256e-05 
## ... Similar to previous best
## Run 5 stress 0.08877044 
## ... Procrustes: rmse 4.420123e-05  max resid 0.0003131291 
## ... Similar to previous best
## Run 6 stress 0.08877042 
## ... Procrustes: rmse 1.808169e-05  max resid 6.198966e-05 
## ... Similar to previous best
## Run 7 stress 0.08877046 
## ... Procrustes: rmse 6.296081e-05  max resid 0.000248557 
## ... Similar to previous best
## Run 8 stress 0.08877039 
## ... New best solution
## ... Procrustes: rmse 1.136998e-05  max resid 4.613626e-05 
## ... Similar to previous best
## Run 9 stress 0.08877039 
## ... Procrustes: rmse 5.552613e-06  max resid 3.790367e-05 
## ... Similar to previous best
## Run 10 stress 0.08877046 
## ... Procrustes: rmse 5.61557e-05  max resid 0.0002991419 
## ... Similar to previous best
## Run 11 stress 0.08877041 
## ... Procrustes: rmse 1.090928e-05  max resid 4.508346e-05 
## ... Similar to previous best
## Run 12 stress 0.08877045 
## ... Procrustes: rmse 5.175765e-05  max resid 0.0002103899 
## ... Similar to previous best
## Run 13 stress 0.08877052 
## ... Procrustes: rmse 9.462948e-05  max resid 0.0006280546 
## ... Similar to previous best
## Run 14 stress 0.08877052 
## ... Procrustes: rmse 4.700974e-05  max resid 0.0001961339 
## ... Similar to previous best
## Run 15 stress 0.0887704 
## ... Procrustes: rmse 1.867596e-05  max resid 0.0001225216 
## ... Similar to previous best
## Run 16 stress 0.08877043 
## ... Procrustes: rmse 1.616716e-05  max resid 7.772941e-05 
## ... Similar to previous best
## Run 17 stress 0.08877054 
## ... Procrustes: rmse 7.179423e-05  max resid 0.0002712936 
## ... Similar to previous best
## Run 18 stress 0.08877052 
## ... Procrustes: rmse 6.902306e-05  max resid 0.0003015362 
## ... Similar to previous best
## Run 19 stress 0.0887704 
## ... Procrustes: rmse 9.809286e-06  max resid 4.207407e-05 
## ... Similar to previous best
## Run 20 stress 0.0887704 
## ... Procrustes: rmse 2.570502e-05  max resid 0.000139491 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09483809 
## Run 1 stress 0.09483761 
## ... New best solution
## ... Procrustes: rmse 0.0001572719  max resid 0.001116642 
## ... Similar to previous best
## Run 2 stress 0.0948418 
## ... Procrustes: rmse 0.001936089  max resid 0.01439276 
## Run 3 stress 0.09483831 
## ... Procrustes: rmse 0.0001906393  max resid 0.001357448 
## ... Similar to previous best
## Run 4 stress 0.09484757 
## ... Procrustes: rmse 0.003040681  max resid 0.02265513 
## Run 5 stress 0.0948389 
## ... Procrustes: rmse 0.0002878993  max resid 0.002066576 
## ... Similar to previous best
## Run 6 stress 0.09485579 
## ... Procrustes: rmse 0.003854468  max resid 0.02868792 
## Run 7 stress 0.09484759 
## ... Procrustes: rmse 0.003042327  max resid 0.02266585 
## Run 8 stress 0.09483834 
## ... Procrustes: rmse 0.000222234  max resid 0.001612226 
## ... Similar to previous best
## Run 9 stress 0.09485255 
## ... Procrustes: rmse 0.003623672  max resid 0.02696925 
## Run 10 stress 0.09485614 
## ... Procrustes: rmse 0.003929633  max resid 0.02924022 
## Run 11 stress 0.09483878 
## ... Procrustes: rmse 0.0002997174  max resid 0.00217378 
## ... Similar to previous best
## Run 12 stress 0.09485145 
## ... Procrustes: rmse 0.003498991  max resid 0.02606732 
## Run 13 stress 0.09485511 
## ... Procrustes: rmse 0.003852453  max resid 0.02866975 
## Run 14 stress 0.09485159 
## ... Procrustes: rmse 0.003527798  max resid 0.02627817 
## Run 15 stress 0.09483803 
## ... Procrustes: rmse 0.0001578844  max resid 0.001128282 
## ... Similar to previous best
## Run 16 stress 0.09485504 
## ... Procrustes: rmse 0.003831363  max resid 0.02850523 
## Run 17 stress 0.09483899 
## ... Procrustes: rmse 0.0003249813  max resid 0.002323756 
## ... Similar to previous best
## Run 18 stress 0.0948496 
## ... Procrustes: rmse 0.003309988  max resid 0.02466139 
## Run 19 stress 0.09485324 
## ... Procrustes: rmse 0.003686152  max resid 0.02744993 
## Run 20 stress 0.09485154 
## ... Procrustes: rmse 0.003435369  max resid 0.02558228 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.06608951 
## Run 1 stress 0.06608957 
## ... Procrustes: rmse 9.596609e-05  max resid 0.0005644808 
## ... Similar to previous best
## Run 2 stress 0.06608992 
## ... Procrustes: rmse 0.0001740889  max resid 0.001024336 
## ... Similar to previous best
## Run 3 stress 0.0660897 
## ... Procrustes: rmse 7.052492e-05  max resid 0.000392195 
## ... Similar to previous best
## Run 4 stress 0.06608971 
## ... Procrustes: rmse 0.000138014  max resid 0.000864539 
## ... Similar to previous best
## Run 5 stress 0.0660896 
## ... Procrustes: rmse 3.378383e-05  max resid 0.0002033554 
## ... Similar to previous best
## Run 6 stress 0.06608994 
## ... Procrustes: rmse 0.0001000638  max resid 0.0005893419 
## ... Similar to previous best
## Run 7 stress 0.1061226 
## Run 8 stress 0.0660898 
## ... Procrustes: rmse 0.0001599026  max resid 0.0009018106 
## ... Similar to previous best
## Run 9 stress 0.06608958 
## ... Procrustes: rmse 4.509987e-05  max resid 0.0002424317 
## ... Similar to previous best
## Run 10 stress 0.06608949 
## ... New best solution
## ... Procrustes: rmse 4.458967e-05  max resid 0.0002774656 
## ... Similar to previous best
## Run 11 stress 0.0660896 
## ... Procrustes: rmse 8.949078e-05  max resid 0.0006007087 
## ... Similar to previous best
## Run 12 stress 0.06608979 
## ... Procrustes: rmse 0.0001274196  max resid 0.0006068881 
## ... Similar to previous best
## Run 13 stress 0.06608949 
## ... New best solution
## ... Procrustes: rmse 4.043232e-05  max resid 0.0002488505 
## ... Similar to previous best
## Run 14 stress 0.06608947 
## ... New best solution
## ... Procrustes: rmse 2.912364e-05  max resid 0.0001880652 
## ... Similar to previous best
## Run 15 stress 0.06608952 
## ... Procrustes: rmse 2.947219e-05  max resid 0.0001504271 
## ... Similar to previous best
## Run 16 stress 0.06608984 
## ... Procrustes: rmse 0.0001284738  max resid 0.0007676231 
## ... Similar to previous best
## Run 17 stress 0.06608958 
## ... Procrustes: rmse 7.510331e-05  max resid 0.0004653102 
## ... Similar to previous best
## Run 18 stress 0.06608985 
## ... Procrustes: rmse 0.0001326414  max resid 0.0008258256 
## ... Similar to previous best
## Run 19 stress 0.06608972 
## ... Procrustes: rmse 9.642526e-05  max resid 0.000540934 
## ... Similar to previous best
## Run 20 stress 0.06608947 
## ... Procrustes: rmse 1.686598e-05  max resid 8.829058e-05 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.1022632 
## Run 1 stress 0.1022629 
## ... New best solution
## ... Procrustes: rmse 8.31549e-05  max resid 0.0002492188 
## ... Similar to previous best
## Run 2 stress 0.1035119 
## Run 3 stress 0.1035086 
## Run 4 stress 0.1035093 
## Run 5 stress 0.1022631 
## ... Procrustes: rmse 0.0001527899  max resid 0.0005272731 
## ... Similar to previous best
## Run 6 stress 0.1022629 
## ... New best solution
## ... Procrustes: rmse 5.691167e-05  max resid 0.0002076609 
## ... Similar to previous best
## Run 7 stress 0.1112375 
## Run 8 stress 0.102263 
## ... Procrustes: rmse 5.354298e-05  max resid 0.0001524059 
## ... Similar to previous best
## Run 9 stress 0.1035077 
## Run 10 stress 0.1112288 
## Run 11 stress 0.1022629 
## ... Procrustes: rmse 7.506715e-05  max resid 0.0002269579 
## ... Similar to previous best
## Run 12 stress 0.1035096 
## Run 13 stress 0.102263 
## ... Procrustes: rmse 3.58014e-05  max resid 0.0001326026 
## ... Similar to previous best
## Run 14 stress 0.111231 
## Run 15 stress 0.1112322 
## Run 16 stress 0.1112338 
## Run 17 stress 0.1035105 
## Run 18 stress 0.1112361 
## Run 19 stress 0.1035095 
## Run 20 stress 0.1022631 
## ... Procrustes: rmse 0.0001024037  max resid 0.0003217259 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09680038 
## Run 1 stress 0.09680006 
## ... New best solution
## ... Procrustes: rmse 0.0002017815  max resid 0.0006003235 
## ... Similar to previous best
## Run 2 stress 0.1121599 
## Run 3 stress 0.09680171 
## ... Procrustes: rmse 0.0003363481  max resid 0.001350219 
## ... Similar to previous best
## Run 4 stress 0.0968 
## ... New best solution
## ... Procrustes: rmse 8.15947e-05  max resid 0.0003518625 
## ... Similar to previous best
## Run 5 stress 0.1088881 
## Run 6 stress 0.09680068 
## ... Procrustes: rmse 0.0002323681  max resid 0.0008498104 
## ... Similar to previous best
## Run 7 stress 0.1121655 
## Run 8 stress 0.1089042 
## Run 9 stress 0.09680024 
## ... Procrustes: rmse 7.398517e-05  max resid 0.0002687824 
## ... Similar to previous best
## Run 10 stress 0.09680012 
## ... Procrustes: rmse 9.488498e-05  max resid 0.0004097133 
## ... Similar to previous best
## Run 11 stress 0.1088904 
## Run 12 stress 0.108897 
## Run 13 stress 0.09680033 
## ... Procrustes: rmse 0.0001610846  max resid 0.0006253535 
## ... Similar to previous best
## Run 14 stress 0.0968001 
## ... Procrustes: rmse 7.130016e-05  max resid 0.0003289378 
## ... Similar to previous best
## Run 15 stress 0.1088777 
## Run 16 stress 0.1088786 
## Run 17 stress 0.09680024 
## ... Procrustes: rmse 0.0001288292  max resid 0.0005002904 
## ... Similar to previous best
## Run 18 stress 0.09680002 
## ... Procrustes: rmse 4.454797e-05  max resid 0.0002306613 
## ... Similar to previous best
## Run 19 stress 0.09680015 
## ... Procrustes: rmse 4.966749e-05  max resid 0.0001792979 
## ... Similar to previous best
## Run 20 stress 0.09680173 
## ... Procrustes: rmse 0.0003957039  max resid 0.001412882 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08730166 
## Run 1 stress 0.08730202 
## ... Procrustes: rmse 0.00015845  max resid 0.001137418 
## ... Similar to previous best
## Run 2 stress 0.08730244 
## ... Procrustes: rmse 0.0002464015  max resid 0.001751035 
## ... Similar to previous best
## Run 3 stress 0.08730184 
## ... Procrustes: rmse 0.0001105158  max resid 0.0007682411 
## ... Similar to previous best
## Run 4 stress 0.08730393 
## ... Procrustes: rmse 0.0004302714  max resid 0.003068614 
## ... Similar to previous best
## Run 5 stress 0.08730273 
## ... Procrustes: rmse 0.00028572  max resid 0.002029081 
## ... Similar to previous best
## Run 6 stress 0.08730239 
## ... Procrustes: rmse 0.0002405943  max resid 0.001706494 
## ... Similar to previous best
## Run 7 stress 0.08730233 
## ... Procrustes: rmse 0.0002418445  max resid 0.001718731 
## ... Similar to previous best
## Run 8 stress 0.08730177 
## ... Procrustes: rmse 0.000101323  max resid 0.0007062679 
## ... Similar to previous best
## Run 9 stress 0.08730235 
## ... Procrustes: rmse 0.0002378418  max resid 0.001680774 
## ... Similar to previous best
## Run 10 stress 0.08730228 
## ... Procrustes: rmse 0.0002269513  max resid 0.00167239 
## ... Similar to previous best
## Run 11 stress 0.08730219 
## ... Procrustes: rmse 0.0002024418  max resid 0.001431484 
## ... Similar to previous best
## Run 12 stress 0.08730308 
## ... Procrustes: rmse 0.0003370074  max resid 0.002398735 
## ... Similar to previous best
## Run 13 stress 0.08730177 
## ... Procrustes: rmse 8.915136e-05  max resid 0.0006496489 
## ... Similar to previous best
## Run 14 stress 0.0873017 
## ... Procrustes: rmse 7.87148e-05  max resid 0.0005676797 
## ... Similar to previous best
## Run 15 stress 0.08730205 
## ... Procrustes: rmse 0.0001935584  max resid 0.001384629 
## ... Similar to previous best
## Run 16 stress 0.08730285 
## ... Procrustes: rmse 0.000299159  max resid 0.002125932 
## ... Similar to previous best
## Run 17 stress 0.08730193 
## ... Procrustes: rmse 0.0001606386  max resid 0.001148359 
## ... Similar to previous best
## Run 18 stress 0.08730177 
## ... Procrustes: rmse 8.037786e-05  max resid 0.0005486387 
## ... Similar to previous best
## Run 19 stress 0.08730207 
## ... Procrustes: rmse 0.0001395937  max resid 0.0009668676 
## ... Similar to previous best
## Run 20 stress 0.08730178 
## ... Procrustes: rmse 0.0001151785  max resid 0.0008303049 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.07255714 
## Run 1 stress 0.07255712 
## ... New best solution
## ... Procrustes: rmse 0.0001156653  max resid 0.000764618 
## ... Similar to previous best
## Run 2 stress 0.07255706 
## ... New best solution
## ... Procrustes: rmse 5.117448e-05  max resid 0.0002878759 
## ... Similar to previous best
## Run 3 stress 0.07255729 
## ... Procrustes: rmse 3.255862e-05  max resid 0.0001367247 
## ... Similar to previous best
## Run 4 stress 0.07255718 
## ... Procrustes: rmse 8.483079e-05  max resid 0.0005978277 
## ... Similar to previous best
## Run 5 stress 0.07255723 
## ... Procrustes: rmse 5.717411e-05  max resid 0.0003026472 
## ... Similar to previous best
## Run 6 stress 0.0725571 
## ... Procrustes: rmse 4.578515e-05  max resid 0.0002814029 
## ... Similar to previous best
## Run 7 stress 0.07255743 
## ... Procrustes: rmse 0.0001432145  max resid 0.001009616 
## ... Similar to previous best
## Run 8 stress 0.07255771 
## ... Procrustes: rmse 0.0001664887  max resid 0.001141647 
## ... Similar to previous best
## Run 9 stress 0.07255706 
## ... Procrustes: rmse 1.558697e-05  max resid 0.0001024634 
## ... Similar to previous best
## Run 10 stress 0.07255706 
## ... Procrustes: rmse 1.169382e-05  max resid 6.922872e-05 
## ... Similar to previous best
## Run 11 stress 0.07255721 
## ... Procrustes: rmse 9.294131e-05  max resid 0.0006560508 
## ... Similar to previous best
## Run 12 stress 0.07255754 
## ... Procrustes: rmse 0.0001609833  max resid 0.001113794 
## ... Similar to previous best
## Run 13 stress 0.07255712 
## ... Procrustes: rmse 5.113539e-05  max resid 0.0003508757 
## ... Similar to previous best
## Run 14 stress 0.07255728 
## ... Procrustes: rmse 9.099091e-05  max resid 0.0006319323 
## ... Similar to previous best
## Run 15 stress 0.07255706 
## ... New best solution
## ... Procrustes: rmse 5.078291e-06  max resid 2.875217e-05 
## ... Similar to previous best
## Run 16 stress 0.07255729 
## ... Procrustes: rmse 0.0001092795  max resid 0.0007526414 
## ... Similar to previous best
## Run 17 stress 0.07255736 
## ... Procrustes: rmse 5.670468e-05  max resid 0.000339332 
## ... Similar to previous best
## Run 18 stress 0.07255706 
## ... Procrustes: rmse 1.615472e-05  max resid 0.0001118949 
## ... Similar to previous best
## Run 19 stress 0.07255741 
## ... Procrustes: rmse 0.0001318341  max resid 0.0008818734 
## ... Similar to previous best
## Run 20 stress 0.07255794 
## ... Procrustes: rmse 0.0002148936  max resid 0.001486881 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.08716137 
## Run 1 stress 0.08716138 
## ... Procrustes: rmse 2.153707e-05  max resid 7.617432e-05 
## ... Similar to previous best
## Run 2 stress 0.08716137 
## ... Procrustes: rmse 1.493027e-05  max resid 5.284686e-05 
## ... Similar to previous best
## Run 3 stress 0.08716137 
## ... Procrustes: rmse 4.371118e-06  max resid 1.675641e-05 
## ... Similar to previous best
## Run 4 stress 0.08716165 
## ... Procrustes: rmse 5.617175e-05  max resid 0.0001771544 
## ... Similar to previous best
## Run 5 stress 0.08716138 
## ... Procrustes: rmse 2.416576e-05  max resid 8.377178e-05 
## ... Similar to previous best
## Run 6 stress 0.08716137 
## ... Procrustes: rmse 1.679799e-05  max resid 5.760035e-05 
## ... Similar to previous best
## Run 7 stress 0.08716141 
## ... Procrustes: rmse 3.656023e-05  max resid 0.0001248472 
## ... Similar to previous best
## Run 8 stress 0.08716142 
## ... Procrustes: rmse 2.851164e-05  max resid 9.182603e-05 
## ... Similar to previous best
## Run 9 stress 0.08716137 
## ... Procrustes: rmse 1.387596e-05  max resid 4.657057e-05 
## ... Similar to previous best
## Run 10 stress 0.08716137 
## ... Procrustes: rmse 1.858916e-05  max resid 6.341768e-05 
## ... Similar to previous best
## Run 11 stress 0.08716137 
## ... Procrustes: rmse 1.49355e-05  max resid 5.166098e-05 
## ... Similar to previous best
## Run 12 stress 0.08716139 
## ... Procrustes: rmse 1.081488e-05  max resid 4.263305e-05 
## ... Similar to previous best
## Run 13 stress 0.08716149 
## ... Procrustes: rmse 7.280441e-05  max resid 0.0002583244 
## ... Similar to previous best
## Run 14 stress 0.08716165 
## ... Procrustes: rmse 0.0001159866  max resid 0.0004038964 
## ... Similar to previous best
## Run 15 stress 0.08716139 
## ... Procrustes: rmse 3.597778e-05  max resid 0.0001349093 
## ... Similar to previous best
## Run 16 stress 0.08716137 
## ... Procrustes: rmse 1.873751e-05  max resid 6.73391e-05 
## ... Similar to previous best
## Run 17 stress 0.08716141 
## ... Procrustes: rmse 4.022367e-05  max resid 0.0001649956 
## ... Similar to previous best
## Run 18 stress 0.08716143 
## ... Procrustes: rmse 5.199414e-05  max resid 0.0001816184 
## ... Similar to previous best
## Run 19 stress 0.08716141 
## ... Procrustes: rmse 4.055753e-05  max resid 0.0001413679 
## ... Similar to previous best
## Run 20 stress 0.08716149 
## ... Procrustes: rmse 7.495187e-05  max resid 0.0002613564 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09356841 
## Run 1 stress 0.09357035 
## ... Procrustes: rmse 0.001036984  max resid 0.005211025 
## ... Similar to previous best
## Run 2 stress 0.09357333 
## ... Procrustes: rmse 0.0008103008  max resid 0.004695749 
## ... Similar to previous best
## Run 3 stress 0.09692557 
## Run 4 stress 0.09358254 
## ... Procrustes: rmse 0.001844986  max resid 0.01021623 
## Run 5 stress 0.09356815 
## ... New best solution
## ... Procrustes: rmse 0.0007470659  max resid 0.004442455 
## ... Similar to previous best
## Run 6 stress 0.09692556 
## Run 7 stress 0.09357082 
## ... Procrustes: rmse 0.0004085872  max resid 0.001922991 
## ... Similar to previous best
## Run 8 stress 0.09357083 
## ... Procrustes: rmse 0.0004094045  max resid 0.001941384 
## ... Similar to previous best
## Run 9 stress 0.09357075 
## ... Procrustes: rmse 0.0004009746  max resid 0.001885179 
## ... Similar to previous best
## Run 10 stress 0.09356852 
## ... Procrustes: rmse 9.689436e-05  max resid 0.000467852 
## ... Similar to previous best
## Run 11 stress 0.09357648 
## ... Procrustes: rmse 0.002034744  max resid 0.01237333 
## Run 12 stress 0.09358526 
## ... Procrustes: rmse 0.002638566  max resid 0.01478808 
## Run 13 stress 0.09357637 
## ... Procrustes: rmse 0.001965432  max resid 0.01307796 
## Run 14 stress 0.09692659 
## Run 15 stress 0.0969257 
## Run 16 stress 0.09357634 
## ... Procrustes: rmse 0.002050736  max resid 0.01265703 
## Run 17 stress 0.09692764 
## Run 18 stress 0.0969287 
## Run 19 stress 0.0969254 
## Run 20 stress 0.09357036 
## ... Procrustes: rmse 0.0003578216  max resid 0.001675408 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.07425622 
## Run 1 stress 0.07425669 
## ... Procrustes: rmse 0.0001060022  max resid 0.0004985191 
## ... Similar to previous best
## Run 2 stress 0.07425746 
## ... Procrustes: rmse 0.0002086398  max resid 0.0009986625 
## ... Similar to previous best
## Run 3 stress 0.07425618 
## ... New best solution
## ... Procrustes: rmse 7.67794e-05  max resid 0.0003454964 
## ... Similar to previous best
## Run 4 stress 0.0742561 
## ... New best solution
## ... Procrustes: rmse 2.256013e-05  max resid 0.0001352918 
## ... Similar to previous best
## Run 5 stress 0.07425608 
## ... New best solution
## ... Procrustes: rmse 4.842773e-05  max resid 0.0002051218 
## ... Similar to previous best
## Run 6 stress 0.07425637 
## ... Procrustes: rmse 0.0001241232  max resid 0.000560555 
## ... Similar to previous best
## Run 7 stress 0.07425606 
## ... New best solution
## ... Procrustes: rmse 9.780353e-06  max resid 3.804323e-05 
## ... Similar to previous best
## Run 8 stress 0.07425719 
## ... Procrustes: rmse 0.0002823296  max resid 0.001312254 
## ... Similar to previous best
## Run 9 stress 0.07425606 
## ... Procrustes: rmse 2.250999e-05  max resid 9.548458e-05 
## ... Similar to previous best
## Run 10 stress 0.07425611 
## ... Procrustes: rmse 3.350103e-05  max resid 0.0001549904 
## ... Similar to previous best
## Run 11 stress 0.07425621 
## ... Procrustes: rmse 8.046465e-05  max resid 0.0003712428 
## ... Similar to previous best
## Run 12 stress 0.07425614 
## ... Procrustes: rmse 8.352501e-05  max resid 0.0003660528 
## ... Similar to previous best
## Run 13 stress 0.07425699 
## ... Procrustes: rmse 0.0002514561  max resid 0.001164952 
## ... Similar to previous best
## Run 14 stress 0.07425676 
## ... Procrustes: rmse 0.0002229114  max resid 0.001029828 
## ... Similar to previous best
## Run 15 stress 0.07425673 
## ... Procrustes: rmse 0.0001729766  max resid 0.000773296 
## ... Similar to previous best
## Run 16 stress 0.07425773 
## ... Procrustes: rmse 0.000326543  max resid 0.001517172 
## ... Similar to previous best
## Run 17 stress 0.07425704 
## ... Procrustes: rmse 0.0002523273  max resid 0.001169519 
## ... Similar to previous best
## Run 18 stress 0.07425611 
## ... Procrustes: rmse 4.175534e-05  max resid 0.0001955961 
## ... Similar to previous best
## Run 19 stress 0.07425659 
## ... Procrustes: rmse 0.0001607866  max resid 0.0007233893 
## ... Similar to previous best
## Run 20 stress 0.07425679 
## ... Procrustes: rmse 0.0002004777  max resid 0.0008967147 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.09457686 
## Run 1 stress 0.09457652 
## ... New best solution
## ... Procrustes: rmse 8.56382e-05  max resid 0.0005394522 
## ... Similar to previous best
## Run 2 stress 0.09457768 
## ... Procrustes: rmse 0.0002082935  max resid 0.001134599 
## ... Similar to previous best
## Run 3 stress 0.09457697 
## ... Procrustes: rmse 0.0003747623  max resid 0.001981177 
## ... Similar to previous best
## Run 4 stress 0.09457786 
## ... Procrustes: rmse 0.0002263038  max resid 0.001323804 
## ... Similar to previous best
## Run 5 stress 0.09457709 
## ... Procrustes: rmse 0.0001051722  max resid 0.0006157543 
## ... Similar to previous best
## Run 6 stress 0.09457785 
## ... Procrustes: rmse 0.0004744894  max resid 0.002482588 
## ... Similar to previous best
## Run 7 stress 0.09457772 
## ... Procrustes: rmse 0.0004886311  max resid 0.00254212 
## ... Similar to previous best
## Run 8 stress 0.09457756 
## ... Procrustes: rmse 0.0004511969  max resid 0.002344732 
## ... Similar to previous best
## Run 9 stress 0.09457691 
## ... Procrustes: rmse 0.0003694528  max resid 0.001950577 
## ... Similar to previous best
## Run 10 stress 0.09457631 
## ... New best solution
## ... Procrustes: rmse 0.000113848  max resid 0.0006225658 
## ... Similar to previous best
## Run 11 stress 0.09457632 
## ... Procrustes: rmse 7.200607e-05  max resid 0.0004055652 
## ... Similar to previous best
## Run 12 stress 0.09457704 
## ... Procrustes: rmse 0.0002789725  max resid 0.001457425 
## ... Similar to previous best
## Run 13 stress 0.09457663 
## ... Procrustes: rmse 0.0001914735  max resid 0.001034559 
## ... Similar to previous best
## Run 14 stress 0.09457638 
## ... Procrustes: rmse 5.882156e-05  max resid 0.0002598129 
## ... Similar to previous best
## Run 15 stress 0.09457765 
## ... Procrustes: rmse 0.0003182443  max resid 0.001821409 
## ... Similar to previous best
## Run 16 stress 0.09457788 
## ... Procrustes: rmse 0.0003857223  max resid 0.001986772 
## ... Similar to previous best
## Run 17 stress 0.0945771 
## ... Procrustes: rmse 0.0002385721  max resid 0.001361465 
## ... Similar to previous best
## Run 18 stress 0.09457673 
## ... Procrustes: rmse 0.0001567104  max resid 0.0008897796 
## ... Similar to previous best
## Run 19 stress 0.09457786 
## ... Procrustes: rmse 0.0003421881  max resid 0.001960654 
## ... Similar to previous best
## Run 20 stress 0.09457684 
## ... Procrustes: rmse 0.0001888611  max resid 0.0010778 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.03145116 
## Run 1 stress 0.03145131 
## ... Procrustes: rmse 3.279728e-05  max resid 0.0001160832 
## ... Similar to previous best
## Run 2 stress 0.03474676 
## Run 3 stress 0.04815295 
## Run 4 stress 0.05138253 
## Run 5 stress 0.03474623 
## Run 6 stress 0.03474749 
## Run 7 stress 0.05082791 
## Run 8 stress 0.03147542 
## ... Procrustes: rmse 0.002119487  max resid 0.01096477 
## Run 9 stress 0.03474655 
## Run 10 stress 0.03145286 
## ... Procrustes: rmse 0.001187134  max resid 0.006103472 
## ... Similar to previous best
## Run 11 stress 0.03308486 
## Run 12 stress 0.03144917 
## ... New best solution
## ... Procrustes: rmse 0.000222058  max resid 0.001091374 
## ... Similar to previous best
## Run 13 stress 0.03240349 
## Run 14 stress 0.03474685 
## Run 15 stress 0.03144975 
## ... Procrustes: rmse 0.0006273487  max resid 0.003125827 
## ... Similar to previous best
## Run 16 stress 0.03144998 
## ... Procrustes: rmse 0.0007184706  max resid 0.00377674 
## ... Similar to previous best
## Run 17 stress 0.0324039 
## Run 18 stress 0.03145163 
## ... Procrustes: rmse 0.0008747037  max resid 0.004542233 
## ... Similar to previous best
## Run 19 stress 0.03240341 
## Run 20 stress 0.03474719 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.632009e-05 
## ... Procrustes: rmse 0.0001699321  max resid 0.0007992366 
## ... Similar to previous best
## Run 2 stress 9.260983e-05 
## ... Procrustes: rmse 0.0001645643  max resid 0.0005972188 
## ... Similar to previous best
## Run 3 stress 9.965867e-05 
## ... Procrustes: rmse 0.0001675049  max resid 0.0007201619 
## ... Similar to previous best
## Run 4 stress 8.114108e-05 
## ... Procrustes: rmse 0.0001559394  max resid 0.0007278782 
## ... Similar to previous best
## Run 5 stress 9.155602e-05 
## ... Procrustes: rmse 0.0001605972  max resid 0.0008314485 
## ... Similar to previous best
## Run 6 stress 9.465339e-05 
## ... Procrustes: rmse 0.0001618903  max resid 0.0007822471 
## ... Similar to previous best
## Run 7 stress 7.221162e-05 
## ... Procrustes: rmse 0.0001343336  max resid 0.000593774 
## ... Similar to previous best
## Run 8 stress 9.971324e-05 
## ... Procrustes: rmse 0.0001660645  max resid 0.0008686937 
## ... Similar to previous best
## Run 9 stress 9.594096e-05 
## ... Procrustes: rmse 0.0001709714  max resid 0.0009947761 
## ... Similar to previous best
## Run 10 stress 9.191044e-05 
## ... Procrustes: rmse 0.0001642345  max resid 0.001007921 
## ... Similar to previous best
## Run 11 stress 9.265873e-05 
## ... Procrustes: rmse 0.0001579337  max resid 0.0006942206 
## ... Similar to previous best
## Run 12 stress 9.89023e-05 
## ... Procrustes: rmse 0.0001733005  max resid 0.0009301558 
## ... Similar to previous best
## Run 13 stress 8.934795e-05 
## ... Procrustes: rmse 0.0001688647  max resid 0.0007043231 
## ... Similar to previous best
## Run 14 stress 9.694868e-05 
## ... Procrustes: rmse 0.0001613317  max resid 0.000621031 
## ... Similar to previous best
## Run 15 stress 8.108469e-05 
## ... Procrustes: rmse 0.0001530404  max resid 0.0008336713 
## ... Similar to previous best
## Run 16 stress 7.745025e-05 
## ... Procrustes: rmse 0.0001475472  max resid 0.0006755637 
## ... Similar to previous best
## Run 17 stress 9.909513e-05 
## ... Procrustes: rmse 0.0001723312  max resid 0.0008152828 
## ... Similar to previous best
## Run 18 stress 9.713091e-05 
## ... Procrustes: rmse 0.0001267474  max resid 0.0007091027 
## ... Similar to previous best
## Run 19 stress 7.785069e-05 
## ... Procrustes: rmse 0.000138654  max resid 0.0006463437 
## ... Similar to previous best
## Run 20 stress 9.473477e-05 
## ... Procrustes: rmse 0.0001637393  max resid 0.000664788 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.782656e-05 
## ... Procrustes: rmse 0.0001600914  max resid 0.0009088318 
## ... Similar to previous best
## Run 2 stress 9.076693e-05 
## ... Procrustes: rmse 0.0001445025  max resid 0.0004463379 
## ... Similar to previous best
## Run 3 stress 9.647686e-05 
## ... Procrustes: rmse 0.0001657638  max resid 0.0006910255 
## ... Similar to previous best
## Run 4 stress 9.793439e-05 
## ... Procrustes: rmse 0.000169358  max resid 0.0009356711 
## ... Similar to previous best
## Run 5 stress 9.501145e-05 
## ... Procrustes: rmse 0.0001727955  max resid 0.0009861154 
## ... Similar to previous best
## Run 6 stress 9.161757e-05 
## ... Procrustes: rmse 0.0001434626  max resid 0.0004841362 
## ... Similar to previous best
## Run 7 stress 8.806723e-05 
## ... Procrustes: rmse 0.0001558155  max resid 0.0008586629 
## ... Similar to previous best
## Run 8 stress 9.834742e-05 
## ... Procrustes: rmse 0.0001668768  max resid 0.0005307136 
## ... Similar to previous best
## Run 9 stress 8.418926e-05 
## ... Procrustes: rmse 0.0001607761  max resid 0.0008779899 
## ... Similar to previous best
## Run 10 stress 9.477751e-05 
## ... Procrustes: rmse 0.000155469  max resid 0.000623608 
## ... Similar to previous best
## Run 11 stress 9.687941e-05 
## ... Procrustes: rmse 0.0001643022  max resid 0.0008180518 
## ... Similar to previous best
## Run 12 stress 9.377217e-05 
## ... Procrustes: rmse 0.0001669683  max resid 0.000816116 
## ... Similar to previous best
## Run 13 stress 9.358112e-05 
## ... Procrustes: rmse 0.0001700118  max resid 0.00106679 
## ... Similar to previous best
## Run 14 stress 9.436939e-05 
## ... Procrustes: rmse 0.0001583334  max resid 0.0004494837 
## ... Similar to previous best
## Run 15 stress 8.350099e-05 
## ... Procrustes: rmse 0.0001386785  max resid 0.0005663992 
## ... Similar to previous best
## Run 16 stress 9.98428e-05 
## ... Procrustes: rmse 0.0001689704  max resid 0.0009424901 
## ... Similar to previous best
## Run 17 stress 9.222838e-05 
## ... Procrustes: rmse 0.0001442069  max resid 0.0005546836 
## ... Similar to previous best
## Run 18 stress 8.963101e-05 
## ... Procrustes: rmse 0.0001636602  max resid 0.0008327575 
## ... Similar to previous best
## Run 19 stress 9.266124e-05 
## ... Procrustes: rmse 0.0001526461  max resid 0.0006198067 
## ... Similar to previous best
## Run 20 stress 8.948156e-05 
## ... Procrustes: rmse 0.0001618322  max resid 0.0006446196 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.389511e-05 
## ... Procrustes: rmse 0.0001710008  max resid 0.0009714308 
## ... Similar to previous best
## Run 2 stress 9.494326e-05 
## ... Procrustes: rmse 0.0001806372  max resid 0.0007274808 
## ... Similar to previous best
## Run 3 stress 9.396603e-05 
## ... Procrustes: rmse 0.0001659193  max resid 0.0008346312 
## ... Similar to previous best
## Run 4 stress 9.376319e-05 
## ... Procrustes: rmse 0.0001562745  max resid 0.0006161703 
## ... Similar to previous best
## Run 5 stress 9.824013e-05 
## ... Procrustes: rmse 0.0001662413  max resid 0.0008024195 
## ... Similar to previous best
## Run 6 stress 8.969292e-05 
## ... Procrustes: rmse 0.0001672052  max resid 0.0006796589 
## ... Similar to previous best
## Run 7 stress 9.729724e-05 
## ... Procrustes: rmse 0.0001757725  max resid 0.001013696 
## ... Similar to previous best
## Run 8 stress 9.830966e-05 
## ... Procrustes: rmse 0.0001692138  max resid 0.001062224 
## ... Similar to previous best
## Run 9 stress 7.712417e-05 
## ... Procrustes: rmse 0.0001118452  max resid 0.0006231916 
## ... Similar to previous best
## Run 10 stress 8.777176e-05 
## ... Procrustes: rmse 0.0001487423  max resid 0.0006648963 
## ... Similar to previous best
## Run 11 stress 9.379748e-05 
## ... Procrustes: rmse 0.0001641003  max resid 0.0009175692 
## ... Similar to previous best
## Run 12 stress 9.619192e-05 
## ... Procrustes: rmse 0.0001792569  max resid 0.0008104087 
## ... Similar to previous best
## Run 13 stress 9.758359e-05 
## ... Procrustes: rmse 0.0001847043  max resid 0.0009897865 
## ... Similar to previous best
## Run 14 stress 9.785982e-05 
## ... Procrustes: rmse 0.0001784962  max resid 0.0007752715 
## ... Similar to previous best
## Run 15 stress 9.24782e-05 
## ... Procrustes: rmse 0.0001675024  max resid 0.0008643654 
## ... Similar to previous best
## Run 16 stress 9.219828e-05 
## ... Procrustes: rmse 0.0001779424  max resid 0.001065759 
## ... Similar to previous best
## Run 17 stress 9.287813e-05 
## ... Procrustes: rmse 0.000176535  max resid 0.000855474 
## ... Similar to previous best
## Run 18 stress 9.631619e-05 
## ... Procrustes: rmse 0.0001779272  max resid 0.0009054911 
## ... Similar to previous best
## Run 19 stress 8.254114e-05 
## ... Procrustes: rmse 0.0001600632  max resid 0.0008835198 
## ... Similar to previous best
## Run 20 stress 9.517273e-05 
## ... Procrustes: rmse 0.0001701944  max resid 0.001058368 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.967443e-05 
## ... Procrustes: rmse 0.0001871324  max resid 0.0008559439 
## ... Similar to previous best
## Run 2 stress 9.166455e-05 
## ... Procrustes: rmse 0.0001542267  max resid 0.0006387039 
## ... Similar to previous best
## Run 3 stress 9.476745e-05 
## ... Procrustes: rmse 0.0001778307  max resid 0.0007284299 
## ... Similar to previous best
## Run 4 stress 9.644968e-05 
## ... Procrustes: rmse 0.0001866326  max resid 0.0009043548 
## ... Similar to previous best
## Run 5 stress 9.366326e-05 
## ... Procrustes: rmse 0.0001684369  max resid 0.0009041758 
## ... Similar to previous best
## Run 6 stress 9.621914e-05 
## ... Procrustes: rmse 0.0001800118  max resid 0.0008702901 
## ... Similar to previous best
## Run 7 stress 9.688422e-05 
## ... Procrustes: rmse 0.0001709049  max resid 0.0007156161 
## ... Similar to previous best
## Run 8 stress 9.811745e-05 
## ... Procrustes: rmse 0.000175149  max resid 0.0008234501 
## ... Similar to previous best
## Run 9 stress 9.316075e-05 
## ... Procrustes: rmse 0.0001788217  max resid 0.0008116632 
## ... Similar to previous best
## Run 10 stress 9.445255e-05 
## ... Procrustes: rmse 0.0001900643  max resid 0.0008028325 
## ... Similar to previous best
## Run 11 stress 9.691711e-05 
## ... Procrustes: rmse 0.0001814941  max resid 0.0008033564 
## ... Similar to previous best
## Run 12 stress 9.94416e-05 
## ... Procrustes: rmse 0.0001821059  max resid 0.0008938197 
## ... Similar to previous best
## Run 13 stress 9.443519e-05 
## ... Procrustes: rmse 0.0001791872  max resid 0.0007701855 
## ... Similar to previous best
## Run 14 stress 9.227803e-05 
## ... Procrustes: rmse 0.0001833004  max resid 0.000655691 
## ... Similar to previous best
## Run 15 stress 9.066071e-05 
## ... Procrustes: rmse 0.0001736596  max resid 0.0008529364 
## ... Similar to previous best
## Run 16 stress 9.968522e-05 
## ... Procrustes: rmse 0.0001797289  max resid 0.0006679259 
## ... Similar to previous best
## Run 17 stress 8.890572e-05 
## ... Procrustes: rmse 0.0001560661  max resid 0.0006960994 
## ... Similar to previous best
## Run 18 stress 9.422499e-05 
## ... Procrustes: rmse 0.00017043  max resid 0.0007555549 
## ... Similar to previous best
## Run 19 stress 9.998956e-05 
## ... Procrustes: rmse 0.0001792095  max resid 0.0009375417 
## ... Similar to previous best
## Run 20 stress 9.97905e-05 
## ... Procrustes: rmse 0.0001885226  max resid 0.0007653317 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.712037e-05 
## ... Procrustes: rmse 0.0002107925  max resid 0.0009715774 
## ... Similar to previous best
## Run 2 stress 9.412747e-05 
## ... Procrustes: rmse 0.0001926185  max resid 0.001109457 
## ... Similar to previous best
## Run 3 stress 9.544353e-05 
## ... Procrustes: rmse 0.0002138345  max resid 0.001405294 
## ... Similar to previous best
## Run 4 stress 9.894342e-05 
## ... Procrustes: rmse 0.0002107077  max resid 0.00116083 
## ... Similar to previous best
## Run 5 stress 9.401533e-05 
## ... Procrustes: rmse 0.0001764736  max resid 0.0005563946 
## ... Similar to previous best
## Run 6 stress 9.408201e-05 
## ... Procrustes: rmse 0.0002179988  max resid 0.001201521 
## ... Similar to previous best
## Run 7 stress 8.582163e-05 
## ... Procrustes: rmse 0.0001850467  max resid 0.001096918 
## ... Similar to previous best
## Run 8 stress 9.804761e-05 
## ... Procrustes: rmse 0.0002087738  max resid 0.0008784205 
## ... Similar to previous best
## Run 9 stress 9.136583e-05 
## ... Procrustes: rmse 0.0002183181  max resid 0.001042261 
## ... Similar to previous best
## Run 10 stress 8.087634e-05 
## ... Procrustes: rmse 0.0001963005  max resid 0.001276537 
## ... Similar to previous best
## Run 11 stress 9.955872e-05 
## ... Procrustes: rmse 0.0001626829  max resid 0.0007910741 
## ... Similar to previous best
## Run 12 stress 9.746458e-05 
## ... Procrustes: rmse 0.0002138063  max resid 0.001415276 
## ... Similar to previous best
## Run 13 stress 9.529235e-05 
## ... Procrustes: rmse 0.0002152088  max resid 0.0009392457 
## ... Similar to previous best
## Run 14 stress 9.740543e-05 
## ... Procrustes: rmse 0.0001790374  max resid 0.0008629879 
## ... Similar to previous best
## Run 15 stress 9.266411e-05 
## ... Procrustes: rmse 0.0001935416  max resid 0.0007210835 
## ... Similar to previous best
## Run 16 stress 9.396621e-05 
## ... Procrustes: rmse 0.0001899526  max resid 0.0007799619 
## ... Similar to previous best
## Run 17 stress 9.998812e-05 
## ... Procrustes: rmse 0.0002287227  max resid 0.0009322135 
## ... Similar to previous best
## Run 18 stress 9.318003e-05 
## ... Procrustes: rmse 0.0002038071  max resid 0.0009629113 
## ... Similar to previous best
## Run 19 stress 9.64176e-05 
## ... Procrustes: rmse 0.0001981528  max resid 0.001037485 
## ... Similar to previous best
## Run 20 stress 9.192169e-05 
## ... Procrustes: rmse 0.0001912103  max resid 0.0007596146 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.179001e-05 
## ... Procrustes: rmse 0.0001715578  max resid 0.000656364 
## ... Similar to previous best
## Run 2 stress 9.168266e-05 
## ... Procrustes: rmse 0.000186514  max resid 0.001138935 
## ... Similar to previous best
## Run 3 stress 9.468798e-05 
## ... Procrustes: rmse 0.0001887245  max resid 0.00120904 
## ... Similar to previous best
## Run 4 stress 8.782093e-05 
## ... Procrustes: rmse 0.0001513998  max resid 0.0006658898 
## ... Similar to previous best
## Run 5 stress 9.169685e-05 
## ... Procrustes: rmse 0.00018135  max resid 0.001186756 
## ... Similar to previous best
## Run 6 stress 9.404251e-05 
## ... Procrustes: rmse 0.0001821897  max resid 0.00092342 
## ... Similar to previous best
## Run 7 stress 9.705609e-05 
## ... Procrustes: rmse 0.0001778024  max resid 0.001134782 
## ... Similar to previous best
## Run 8 stress 9.419114e-05 
## ... Procrustes: rmse 0.0001671739  max resid 0.000859483 
## ... Similar to previous best
## Run 9 stress 9.887112e-05 
## ... Procrustes: rmse 0.0001836333  max resid 0.0008795596 
## ... Similar to previous best
## Run 10 stress 8.777573e-05 
## ... Procrustes: rmse 0.0001817728  max resid 0.00117603 
## ... Similar to previous best
## Run 11 stress 9.298384e-05 
## ... Procrustes: rmse 0.0001786016  max resid 0.001064788 
## ... Similar to previous best
## Run 12 stress 9.770213e-05 
## ... Procrustes: rmse 0.00018721  max resid 0.001187054 
## ... Similar to previous best
## Run 13 stress 9.262476e-05 
## ... Procrustes: rmse 0.0001837213  max resid 0.001197153 
## ... Similar to previous best
## Run 14 stress 9.967561e-05 
## ... Procrustes: rmse 0.0001982104  max resid 0.001278432 
## ... Similar to previous best
## Run 15 stress 9.63867e-05 
## ... Procrustes: rmse 0.0001847329  max resid 0.001164215 
## ... Similar to previous best
## Run 16 stress 9.435399e-05 
## ... Procrustes: rmse 0.0001891634  max resid 0.001216534 
## ... Similar to previous best
## Run 17 stress 9.725791e-05 
## ... Procrustes: rmse 0.0001898888  max resid 0.001210536 
## ... Similar to previous best
## Run 18 stress 9.591623e-05 
## ... Procrustes: rmse 0.0001809856  max resid 0.001056011 
## ... Similar to previous best
## Run 19 stress 9.346098e-05 
## ... Procrustes: rmse 0.0001873273  max resid 0.00120528 
## ... Similar to previous best
## Run 20 stress 9.143962e-05 
## ... Procrustes: rmse 0.0001694691  max resid 0.000911081 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.314284e-05 
## ... Procrustes: rmse 0.0001525683  max resid 0.0007071475 
## ... Similar to previous best
## Run 2 stress 8.617958e-05 
## ... Procrustes: rmse 0.0001386558  max resid 0.0005204851 
## ... Similar to previous best
## Run 3 stress 9.844571e-05 
## ... Procrustes: rmse 0.000158191  max resid 0.0006689462 
## ... Similar to previous best
## Run 4 stress 9.934764e-05 
## ... Procrustes: rmse 0.0001584433  max resid 0.0007665075 
## ... Similar to previous best
## Run 5 stress 9.700439e-05 
## ... Procrustes: rmse 0.0001426505  max resid 0.0004993978 
## ... Similar to previous best
## Run 6 stress 8.76813e-05 
## ... Procrustes: rmse 0.0001376287  max resid 0.0005870343 
## ... Similar to previous best
## Run 7 stress 8.998935e-05 
## ... Procrustes: rmse 0.0001470729  max resid 0.0005132984 
## ... Similar to previous best
## Run 8 stress 9.595722e-05 
## ... Procrustes: rmse 0.0001565644  max resid 0.0007258068 
## ... Similar to previous best
## Run 9 stress 9.312415e-05 
## ... Procrustes: rmse 0.0001608595  max resid 0.0008114967 
## ... Similar to previous best
## Run 10 stress 8.720205e-05 
## ... Procrustes: rmse 0.0001261678  max resid 0.0003998242 
## ... Similar to previous best
## Run 11 stress 8.883454e-05 
## ... Procrustes: rmse 0.0001530222  max resid 0.0006981399 
## ... Similar to previous best
## Run 12 stress 9.490853e-05 
## ... Procrustes: rmse 0.0001613058  max resid 0.0006562207 
## ... Similar to previous best
## Run 13 stress 8.914309e-05 
## ... Procrustes: rmse 0.000135389  max resid 0.0004877766 
## ... Similar to previous best
## Run 14 stress 9.260007e-05 
## ... Procrustes: rmse 0.0001604979  max resid 0.0006762393 
## ... Similar to previous best
## Run 15 stress 9.116654e-05 
## ... Procrustes: rmse 0.0001435535  max resid 0.0005730897 
## ... Similar to previous best
## Run 16 stress 9.901248e-05 
## ... Procrustes: rmse 0.0001641883  max resid 0.0007650489 
## ... Similar to previous best
## Run 17 stress 9.259275e-05 
## ... Procrustes: rmse 0.0001445003  max resid 0.0007918013 
## ... Similar to previous best
## Run 18 stress 8.84548e-05 
## ... Procrustes: rmse 0.0001352404  max resid 0.0004965703 
## ... Similar to previous best
## Run 19 stress 8.910437e-05 
## ... Procrustes: rmse 0.0001505545  max resid 0.0007594997 
## ... Similar to previous best
## Run 20 stress 9.561313e-05 
## ... Procrustes: rmse 0.0001445956  max resid 0.0005503438 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.953798e-05 
## ... Procrustes: rmse 0.0001250762  max resid 0.0006645469 
## ... Similar to previous best
## Run 2 stress 9.897032e-05 
## ... Procrustes: rmse 0.000168178  max resid 0.0007345901 
## ... Similar to previous best
## Run 3 stress 8.738231e-05 
## ... Procrustes: rmse 0.0001501629  max resid 0.0007506826 
## ... Similar to previous best
## Run 4 stress 9.645719e-05 
## ... Procrustes: rmse 0.000160689  max resid 0.0006844552 
## ... Similar to previous best
## Run 5 stress 9.893987e-05 
## ... Procrustes: rmse 0.0001619722  max resid 0.0007208596 
## ... Similar to previous best
## Run 6 stress 9.720148e-05 
## ... Procrustes: rmse 0.0001667237  max resid 0.0007254331 
## ... Similar to previous best
## Run 7 stress 9.58258e-05 
## ... Procrustes: rmse 0.0001649641  max resid 0.0006047028 
## ... Similar to previous best
## Run 8 stress 9.024676e-05 
## ... Procrustes: rmse 0.0001544715  max resid 0.0006548625 
## ... Similar to previous best
## Run 9 stress 9.621605e-05 
## ... Procrustes: rmse 0.0001606916  max resid 0.0009223183 
## ... Similar to previous best
## Run 10 stress 9.266343e-05 
## ... Procrustes: rmse 0.000152446  max resid 0.0006219466 
## ... Similar to previous best
## Run 11 stress 9.425241e-05 
## ... Procrustes: rmse 0.0001551398  max resid 0.000585227 
## ... Similar to previous best
## Run 12 stress 8.813997e-05 
## ... Procrustes: rmse 0.0001423901  max resid 0.0006058469 
## ... Similar to previous best
## Run 13 stress 9.424037e-05 
## ... Procrustes: rmse 0.0001622841  max resid 0.0006700055 
## ... Similar to previous best
## Run 14 stress 9.309612e-05 
## ... Procrustes: rmse 0.0001595226  max resid 0.0009292715 
## ... Similar to previous best
## Run 15 stress 9.416644e-05 
## ... Procrustes: rmse 0.0001450794  max resid 0.000740914 
## ... Similar to previous best
## Run 16 stress 9.995661e-05 
## ... Procrustes: rmse 0.000163182  max resid 0.000810608 
## ... Similar to previous best
## Run 17 stress 9.473692e-05 
## ... Procrustes: rmse 0.0001472164  max resid 0.0007717997 
## ... Similar to previous best
## Run 18 stress 9.512078e-05 
## ... Procrustes: rmse 0.0001540778  max resid 0.0006470059 
## ... Similar to previous best
## Run 19 stress 9.764041e-05 
## ... Procrustes: rmse 0.0001618791  max resid 0.0008202067 
## ... Similar to previous best
## Run 20 stress 8.977656e-05 
## ... Procrustes: rmse 0.0001572395  max resid 0.0008068601 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.176993e-05 
## ... Procrustes: rmse 0.0001569411  max resid 0.0004923581 
## ... Similar to previous best
## Run 2 stress 9.938426e-05 
## ... Procrustes: rmse 0.0001744714  max resid 0.0008646477 
## ... Similar to previous best
## Run 3 stress 8.900468e-05 
## ... Procrustes: rmse 0.0001686778  max resid 0.000705338 
## ... Similar to previous best
## Run 4 stress 9.100232e-05 
## ... Procrustes: rmse 0.0001631245  max resid 0.0006433314 
## ... Similar to previous best
## Run 5 stress 9.271507e-05 
## ... Procrustes: rmse 0.0001743156  max resid 0.0007134257 
## ... Similar to previous best
## Run 6 stress 9.994043e-05 
## ... Procrustes: rmse 0.0001673623  max resid 0.0005236472 
## ... Similar to previous best
## Run 7 stress 8.82342e-05 
## ... Procrustes: rmse 0.0001626308  max resid 0.0006406149 
## ... Similar to previous best
## Run 8 stress 9.64072e-05 
## ... Procrustes: rmse 0.0001633871  max resid 0.0004982961 
## ... Similar to previous best
## Run 9 stress 9.37467e-05 
## ... Procrustes: rmse 0.0001724923  max resid 0.0006651361 
## ... Similar to previous best
## Run 10 stress 9.538347e-05 
## ... Procrustes: rmse 0.000167565  max resid 0.0006884888 
## ... Similar to previous best
## Run 11 stress 9.268107e-05 
## ... Procrustes: rmse 0.0001765603  max resid 0.000751054 
## ... Similar to previous best
## Run 12 stress 9.490569e-05 
## ... Procrustes: rmse 0.0001705477  max resid 0.0008227129 
## ... Similar to previous best
## Run 13 stress 9.327552e-05 
## ... Procrustes: rmse 0.0001525721  max resid 0.0005821558 
## ... Similar to previous best
## Run 14 stress 9.522225e-05 
## ... Procrustes: rmse 0.0001819285  max resid 0.0007130552 
## ... Similar to previous best
## Run 15 stress 9.555489e-05 
## ... Procrustes: rmse 0.0001704682  max resid 0.0005456251 
## ... Similar to previous best
## Run 16 stress 9.021962e-05 
## ... Procrustes: rmse 0.0001688163  max resid 0.0006451865 
## ... Similar to previous best
## Run 17 stress 9.778557e-05 
## ... Procrustes: rmse 0.0001919495  max resid 0.0008276186 
## ... Similar to previous best
## Run 18 stress 9.463289e-05 
## ... Procrustes: rmse 0.0001803474  max resid 0.0008128766 
## ... Similar to previous best
## Run 19 stress 9.942718e-05 
## ... Procrustes: rmse 0.0001871567  max resid 0.0007999196 
## ... Similar to previous best
## Run 20 stress 9.976818e-05 
## ... Procrustes: rmse 0.0001660427  max resid 0.000674745 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 8.292071e-05 
## ... Procrustes: rmse 0.0001646441  max resid 0.001008409 
## ... Similar to previous best
## Run 2 stress 9.053756e-05 
## ... Procrustes: rmse 0.0001497594  max resid 0.0007220566 
## ... Similar to previous best
## Run 3 stress 9.733385e-05 
## ... Procrustes: rmse 0.0001682917  max resid 0.0008998098 
## ... Similar to previous best
## Run 4 stress 9.105981e-05 
## ... Procrustes: rmse 0.0001592523  max resid 0.0009892982 
## ... Similar to previous best
## Run 5 stress 9.576138e-05 
## ... Procrustes: rmse 0.0001785338  max resid 0.00101289 
## ... Similar to previous best
## Run 6 stress 9.580732e-05 
## ... Procrustes: rmse 0.000179181  max resid 0.001111062 
## ... Similar to previous best
## Run 7 stress 9.390469e-05 
## ... Procrustes: rmse 0.000178446  max resid 0.001022936 
## ... Similar to previous best
## Run 8 stress 9.476021e-05 
## ... Procrustes: rmse 0.0001746796  max resid 0.000758582 
## ... Similar to previous best
## Run 9 stress 8.949982e-05 
## ... Procrustes: rmse 0.0001687957  max resid 0.001058815 
## ... Similar to previous best
## Run 10 stress 9.7765e-05 
## ... Procrustes: rmse 0.0001651728  max resid 0.0009560604 
## ... Similar to previous best
## Run 11 stress 9.410198e-05 
## ... Procrustes: rmse 0.0001651964  max resid 0.0006974452 
## ... Similar to previous best
## Run 12 stress 9.250919e-05 
## ... Procrustes: rmse 0.0001730233  max resid 0.0009564419 
## ... Similar to previous best
## Run 13 stress 9.424086e-05 
## ... Procrustes: rmse 0.0001742444  max resid 0.001101114 
## ... Similar to previous best
## Run 14 stress 9.942006e-05 
## ... Procrustes: rmse 0.0001792702  max resid 0.001032862 
## ... Similar to previous best
## Run 15 stress 9.530946e-05 
## ... Procrustes: rmse 0.0001547875  max resid 0.000904823 
## ... Similar to previous best
## Run 16 stress 9.756285e-05 
## ... Procrustes: rmse 0.0001629167  max resid 0.0006162124 
## ... Similar to previous best
## Run 17 stress 9.438744e-05 
## ... Procrustes: rmse 0.0001712561  max resid 0.001010591 
## ... Similar to previous best
## Run 18 stress 9.717785e-05 
## ... Procrustes: rmse 0.0001750524  max resid 0.001120398 
## ... Similar to previous best
## Run 19 stress 9.263621e-05 
## ... Procrustes: rmse 0.0001600663  max resid 0.0006519888 
## ... Similar to previous best
## Run 20 stress 9.796413e-05 
## ... Procrustes: rmse 0.0001839554  max resid 0.001012526 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.332938e-05 
## ... Procrustes: rmse 0.0001423511  max resid 0.0005998921 
## ... Similar to previous best
## Run 2 stress 9.820404e-05 
## ... Procrustes: rmse 0.00015979  max resid 0.0007882767 
## ... Similar to previous best
## Run 3 stress 9.694442e-05 
## ... Procrustes: rmse 0.0001530463  max resid 0.0006535466 
## ... Similar to previous best
## Run 4 stress 8.271235e-05 
## ... Procrustes: rmse 0.0001122218  max resid 0.0003492946 
## ... Similar to previous best
## Run 5 stress 9.824076e-05 
## ... Procrustes: rmse 0.0001595765  max resid 0.0008476137 
## ... Similar to previous best
## Run 6 stress 8.685583e-05 
## ... Procrustes: rmse 0.0001361459  max resid 0.0008122754 
## ... Similar to previous best
## Run 7 stress 9.002127e-05 
## ... Procrustes: rmse 0.0001452885  max resid 0.0005802017 
## ... Similar to previous best
## Run 8 stress 8.853637e-05 
## ... Procrustes: rmse 0.0001493444  max resid 0.0006852346 
## ... Similar to previous best
## Run 9 stress 9.218078e-05 
## ... Procrustes: rmse 0.0001486209  max resid 0.0005723627 
## ... Similar to previous best
## Run 10 stress 7.342554e-05 
## ... Procrustes: rmse 0.0001375158  max resid 0.0006450302 
## ... Similar to previous best
## Run 11 stress 9.607061e-05 
## ... Procrustes: rmse 0.000151752  max resid 0.0006111509 
## ... Similar to previous best
## Run 12 stress 8.888982e-05 
## ... Procrustes: rmse 0.0001426033  max resid 0.0006477908 
## ... Similar to previous best
## Run 13 stress 9.558613e-05 
## ... Procrustes: rmse 0.0001596161  max resid 0.0008840523 
## ... Similar to previous best
## Run 14 stress 9.805032e-05 
## ... Procrustes: rmse 0.0001450941  max resid 0.0007207976 
## ... Similar to previous best
## Run 15 stress 9.823204e-05 
## ... Procrustes: rmse 0.0001630558  max resid 0.0005398762 
## ... Similar to previous best
## Run 16 stress 9.627809e-05 
## ... Procrustes: rmse 0.0001526926  max resid 0.0006800156 
## ... Similar to previous best
## Run 17 stress 9.044681e-05 
## ... Procrustes: rmse 0.0001433337  max resid 0.0006748812 
## ... Similar to previous best
## Run 18 stress 9.849024e-05 
## ... Procrustes: rmse 0.0001531498  max resid 0.0004921265 
## ... Similar to previous best
## Run 19 stress 9.303421e-05 
## ... Procrustes: rmse 0.0001542314  max resid 0.0006190849 
## ... Similar to previous best
## Run 20 stress 9.582818e-05 
## ... Procrustes: rmse 0.0001493425  max resid 0.0006519312 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.863978e-05 
## ... Procrustes: rmse 0.0001976422  max resid 0.0008990854 
## ... Similar to previous best
## Run 2 stress 9.468572e-05 
## ... Procrustes: rmse 0.0001970131  max resid 0.001252785 
## ... Similar to previous best
## Run 3 stress 8.964282e-05 
## ... Procrustes: rmse 0.000194152  max resid 0.001025989 
## ... Similar to previous best
## Run 4 stress 9.7727e-05 
## ... Procrustes: rmse 0.0002038204  max resid 0.001195048 
## ... Similar to previous best
## Run 5 stress 9.640438e-05 
## ... Procrustes: rmse 0.0002012676  max resid 0.001180226 
## ... Similar to previous best
## Run 6 stress 9.24531e-05 
## ... Procrustes: rmse 0.0001970826  max resid 0.00108177 
## ... Similar to previous best
## Run 7 stress 9.887792e-05 
## ... Procrustes: rmse 0.0001971265  max resid 0.00091411 
## ... Similar to previous best
## Run 8 stress 9.089513e-05 
## ... Procrustes: rmse 0.0001798707  max resid 0.0007747707 
## ... Similar to previous best
## Run 9 stress 9.915118e-05 
## ... Procrustes: rmse 0.0001963105  max resid 0.000783081 
## ... Similar to previous best
## Run 10 stress 8.948078e-05 
## ... Procrustes: rmse 0.000194616  max resid 0.001173585 
## ... Similar to previous best
## Run 11 stress 7.468487e-05 
## ... Procrustes: rmse 0.0001554162  max resid 0.0006308797 
## ... Similar to previous best
## Run 12 stress 9.609251e-05 
## ... Procrustes: rmse 0.0001954527  max resid 0.001010178 
## ... Similar to previous best
## Run 13 stress 9.118097e-05 
## ... Procrustes: rmse 0.00016941  max resid 0.0009381133 
## ... Similar to previous best
## Run 14 stress 9.726257e-05 
## ... Procrustes: rmse 0.0001833585  max resid 0.001053608 
## ... Similar to previous best
## Run 15 stress 8.755507e-05 
## ... Procrustes: rmse 0.0001595857  max resid 0.0008527108 
## ... Similar to previous best
## Run 16 stress 8.375952e-05 
## ... Procrustes: rmse 0.0001837398  max resid 0.001094152 
## ... Similar to previous best
## Run 17 stress 9.44415e-05 
## ... Procrustes: rmse 0.000200246  max resid 0.001247633 
## ... Similar to previous best
## Run 18 stress 8.940751e-05 
## ... Procrustes: rmse 0.0001795998  max resid 0.0007271841 
## ... Similar to previous best
## Run 19 stress 8.873416e-05 
## ... Procrustes: rmse 0.0001920964  max resid 0.001185693 
## ... Similar to previous best
## Run 20 stress 8.319685e-05 
## ... Procrustes: rmse 0.0001811019  max resid 0.0008914238 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.757001e-05 
## ... Procrustes: rmse 0.0001853965  max resid 0.001092632 
## ... Similar to previous best
## Run 2 stress 9.453763e-05 
## ... Procrustes: rmse 0.0002027454  max resid 0.001301817 
## ... Similar to previous best
## Run 3 stress 9.38688e-05 
## ... Procrustes: rmse 0.0001783117  max resid 0.0007701467 
## ... Similar to previous best
## Run 4 stress 9.567536e-05 
## ... Procrustes: rmse 0.0001936517  max resid 0.000959014 
## ... Similar to previous best
## Run 5 stress 8.481214e-05 
## ... Procrustes: rmse 0.0001849685  max resid 0.001191662 
## ... Similar to previous best
## Run 6 stress 9.909071e-05 
## ... Procrustes: rmse 0.0002021888  max resid 0.001259856 
## ... Similar to previous best
## Run 7 stress 9.325068e-05 
## ... Procrustes: rmse 0.0001953224  max resid 0.001205792 
## ... Similar to previous best
## Run 8 stress 9.423625e-05 
## ... Procrustes: rmse 0.0002016055  max resid 0.001273471 
## ... Similar to previous best
## Run 9 stress 8.521574e-05 
## ... Procrustes: rmse 0.0001853893  max resid 0.001178392 
## ... Similar to previous best
## Run 10 stress 9.91969e-05 
## ... Procrustes: rmse 0.0001974456  max resid 0.001056181 
## ... Similar to previous best
## Run 11 stress 9.738758e-05 
## ... Procrustes: rmse 0.0002044362  max resid 0.001300388 
## ... Similar to previous best
## Run 12 stress 9.399855e-05 
## ... Procrustes: rmse 0.0002013634  max resid 0.001219525 
## ... Similar to previous best
## Run 13 stress 8.951858e-05 
## ... Procrustes: rmse 0.0001646951  max resid 0.0006011829 
## ... Similar to previous best
## Run 14 stress 9.744844e-05 
## ... Procrustes: rmse 0.0002085771  max resid 0.001331351 
## ... Similar to previous best
## Run 15 stress 9.788644e-05 
## ... Procrustes: rmse 0.0001820981  max resid 0.0007902638 
## ... Similar to previous best
## Run 16 stress 9.06152e-05 
## ... Procrustes: rmse 0.0001597005  max resid 0.0007122259 
## ... Similar to previous best
## Run 17 stress 9.763373e-05 
## ... Procrustes: rmse 0.0002062307  max resid 0.001071183 
## ... Similar to previous best
## Run 18 stress 9.580241e-05 
## ... Procrustes: rmse 0.0001958517  max resid 0.001259581 
## ... Similar to previous best
## Run 19 stress 9.440154e-05 
## ... Procrustes: rmse 0.0002044709  max resid 0.001297088 
## ... Similar to previous best
## Run 20 stress 9.165545e-05 
## ... Procrustes: rmse 0.0001900393  max resid 0.0009164142 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.130925e-05 
## ... Procrustes: rmse 0.0001639041  max resid 0.0009553365 
## ... Similar to previous best
## Run 2 stress 9.374097e-05 
## ... Procrustes: rmse 0.0001659953  max resid 0.0008549286 
## ... Similar to previous best
## Run 3 stress 9.784011e-05 
## ... Procrustes: rmse 0.0001750741  max resid 0.0006160365 
## ... Similar to previous best
## Run 4 stress 9.071235e-05 
## ... Procrustes: rmse 0.0001596437  max resid 0.0004914712 
## ... Similar to previous best
## Run 5 stress 8.373165e-05 
## ... Procrustes: rmse 0.0001451953  max resid 0.0007619207 
## ... Similar to previous best
## Run 6 stress 9.205811e-05 
## ... Procrustes: rmse 0.0001596382  max resid 0.0007643853 
## ... Similar to previous best
## Run 7 stress 8.9712e-05 
## ... Procrustes: rmse 0.0001627812  max resid 0.0008149592 
## ... Similar to previous best
## Run 8 stress 9.621993e-05 
## ... Procrustes: rmse 0.0001653655  max resid 0.000634581 
## ... Similar to previous best
## Run 9 stress 8.922069e-05 
## ... Procrustes: rmse 0.0001585927  max resid 0.0005715313 
## ... Similar to previous best
## Run 10 stress 9.155514e-05 
## ... Procrustes: rmse 0.000161576  max resid 0.0005297578 
## ... Similar to previous best
## Run 11 stress 8.879908e-05 
## ... Procrustes: rmse 0.000156885  max resid 0.0006951626 
## ... Similar to previous best
## Run 12 stress 9.24787e-05 
## ... Procrustes: rmse 0.0001501981  max resid 0.0007374116 
## ... Similar to previous best
## Run 13 stress 9.907401e-05 
## ... Procrustes: rmse 0.000163998  max resid 0.0007818867 
## ... Similar to previous best
## Run 14 stress 9.208765e-05 
## ... Procrustes: rmse 0.0001535368  max resid 0.0008985849 
## ... Similar to previous best
## Run 15 stress 7.33595e-05 
## ... Procrustes: rmse 0.0001447161  max resid 0.0007508668 
## ... Similar to previous best
## Run 16 stress 9.538816e-05 
## ... Procrustes: rmse 0.0001693383  max resid 0.0006788203 
## ... Similar to previous best
## Run 17 stress 9.887238e-05 
## ... Procrustes: rmse 0.0001704297  max resid 0.0007917928 
## ... Similar to previous best
## Run 18 stress 9.789994e-05 
## ... Procrustes: rmse 0.0001666522  max resid 0.0009223587 
## ... Similar to previous best
## Run 19 stress 9.165087e-05 
## ... Procrustes: rmse 0.0001648073  max resid 0.0009122313 
## ... Similar to previous best
## Run 20 stress 9.239366e-05 
## ... Procrustes: rmse 0.0001572819  max resid 0.0006177112 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 8.941608e-05 
## ... Procrustes: rmse 0.0001837354  max resid 0.0008906608 
## ... Similar to previous best
## Run 2 stress 9.306644e-05 
## ... Procrustes: rmse 0.0002106607  max resid 0.001105085 
## ... Similar to previous best
## Run 3 stress 8.459655e-05 
## ... Procrustes: rmse 0.0002066391  max resid 0.001094598 
## ... Similar to previous best
## Run 4 stress 9.355981e-05 
## ... Procrustes: rmse 0.000206327  max resid 0.001003315 
## ... Similar to previous best
## Run 5 stress 9.280859e-05 
## ... Procrustes: rmse 0.0002162015  max resid 0.0009488946 
## ... Similar to previous best
## Run 6 stress 9.579913e-05 
## ... Procrustes: rmse 0.0002147183  max resid 0.001192619 
## ... Similar to previous best
## Run 7 stress 9.471056e-05 
## ... Procrustes: rmse 0.0001794488  max resid 0.0009127528 
## ... Similar to previous best
## Run 8 stress 9.322145e-05 
## ... Procrustes: rmse 0.000211718  max resid 0.001076408 
## ... Similar to previous best
## Run 9 stress 9.447091e-05 
## ... Procrustes: rmse 0.0002008526  max resid 0.001018116 
## ... Similar to previous best
## Run 10 stress 9.531993e-05 
## ... Procrustes: rmse 0.0001909259  max resid 0.000766897 
## ... Similar to previous best
## Run 11 stress 9.291797e-05 
## ... Procrustes: rmse 0.0002035065  max resid 0.0009886107 
## ... Similar to previous best
## Run 12 stress 9.880837e-05 
## ... Procrustes: rmse 0.0002208746  max resid 0.00119455 
## ... Similar to previous best
## Run 13 stress 9.972902e-05 
## ... Procrustes: rmse 0.0002158097  max resid 0.001172429 
## ... Similar to previous best
## Run 14 stress 9.798934e-05 
## ... Procrustes: rmse 0.0002165157  max resid 0.001259317 
## ... Similar to previous best
## Run 15 stress 9.245476e-05 
## ... Procrustes: rmse 0.0002074022  max resid 0.000931226 
## ... Similar to previous best
## Run 16 stress 9.165221e-05 
## ... Procrustes: rmse 0.0002089308  max resid 0.00119207 
## ... Similar to previous best
## Run 17 stress 9.652448e-05 
## ... Procrustes: rmse 0.0002048194  max resid 0.001131656 
## ... Similar to previous best
## Run 18 stress 9.599436e-05 
## ... Procrustes: rmse 0.0002059033  max resid 0.00111306 
## ... Similar to previous best
## Run 19 stress 9.020018e-05 
## ... Procrustes: rmse 0.0001922931  max resid 0.0009747292 
## ... Similar to previous best
## Run 20 stress 9.639381e-05 
## ... Procrustes: rmse 0.0001808645  max resid 0.0009034467 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.675274e-05 
## ... Procrustes: rmse 0.0001474127  max resid 0.0006114136 
## ... Similar to previous best
## Run 2 stress 8.710806e-05 
## ... Procrustes: rmse 0.0001211781  max resid 0.000483406 
## ... Similar to previous best
## Run 3 stress 8.83613e-05 
## ... Procrustes: rmse 0.0001386906  max resid 0.000658031 
## ... Similar to previous best
## Run 4 stress 9.814584e-05 
## ... Procrustes: rmse 0.0001491844  max resid 0.0007598175 
## ... Similar to previous best
## Run 5 stress 8.982452e-05 
## ... Procrustes: rmse 0.0001377242  max resid 0.0006431465 
## ... Similar to previous best
## Run 6 stress 9.426326e-05 
## ... Procrustes: rmse 0.0001424673  max resid 0.0006258483 
## ... Similar to previous best
## Run 7 stress 9.142398e-05 
## ... Procrustes: rmse 0.0001486089  max resid 0.0005396711 
## ... Similar to previous best
## Run 8 stress 9.834186e-05 
## ... Procrustes: rmse 0.0001482625  max resid 0.0007411069 
## ... Similar to previous best
## Run 9 stress 8.782967e-05 
## ... Procrustes: rmse 0.0001447565  max resid 0.0006508951 
## ... Similar to previous best
## Run 10 stress 9.904619e-05 
## ... Procrustes: rmse 0.0001586379  max resid 0.0008285393 
## ... Similar to previous best
## Run 11 stress 9.798492e-05 
## ... Procrustes: rmse 0.0001466893  max resid 0.0007151414 
## ... Similar to previous best
## Run 12 stress 9.488424e-05 
## ... Procrustes: rmse 0.0001616092  max resid 0.0007099414 
## ... Similar to previous best
## Run 13 stress 9.822071e-05 
## ... Procrustes: rmse 0.000153158  max resid 0.0005491903 
## ... Similar to previous best
## Run 14 stress 9.414095e-05 
## ... Procrustes: rmse 0.0001485736  max resid 0.000693955 
## ... Similar to previous best
## Run 15 stress 7.687833e-05 
## ... Procrustes: rmse 0.0001284169  max resid 0.0003425519 
## ... Similar to previous best
## Run 16 stress 8.895631e-05 
## ... Procrustes: rmse 0.0001423911  max resid 0.0006102359 
## ... Similar to previous best
## Run 17 stress 9.959534e-05 
## ... Procrustes: rmse 0.0001549481  max resid 0.0006427647 
## ... Similar to previous best
## Run 18 stress 9.330242e-05 
## ... Procrustes: rmse 0.0001409305  max resid 0.0005454801 
## ... Similar to previous best
## Run 19 stress 9.854155e-05 
## ... Procrustes: rmse 0.0001565172  max resid 0.0007147049 
## ... Similar to previous best
## Run 20 stress 9.224031e-05 
## ... Procrustes: rmse 0.0001510563  max resid 0.000622836 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.163784e-05 
## ... Procrustes: rmse 0.0001554733  max resid 0.0006231112 
## ... Similar to previous best
## Run 2 stress 9.499448e-05 
## ... Procrustes: rmse 0.0001646863  max resid 0.000512596 
## ... Similar to previous best
## Run 3 stress 9.319796e-05 
## ... Procrustes: rmse 0.000160228  max resid 0.0006738383 
## ... Similar to previous best
## Run 4 stress 8.755533e-05 
## ... Procrustes: rmse 0.000137528  max resid 0.0004393724 
## ... Similar to previous best
## Run 5 stress 9.141695e-05 
## ... Procrustes: rmse 0.0001574477  max resid 0.0007714386 
## ... Similar to previous best
## Run 6 stress 9.756116e-05 
## ... Procrustes: rmse 0.0001633256  max resid 0.000666908 
## ... Similar to previous best
## Run 7 stress 9.656383e-05 
## ... Procrustes: rmse 0.0001639304  max resid 0.000769515 
## ... Similar to previous best
## Run 8 stress 9.959298e-05 
## ... Procrustes: rmse 0.0001649451  max resid 0.0006951603 
## ... Similar to previous best
## Run 9 stress 9.092127e-05 
## ... Procrustes: rmse 0.0001589308  max resid 0.0005164822 
## ... Similar to previous best
## Run 10 stress 9.754567e-05 
## ... Procrustes: rmse 0.0001595415  max resid 0.0006085249 
## ... Similar to previous best
## Run 11 stress 9.28516e-05 
## ... Procrustes: rmse 0.0001527778  max resid 0.00041233 
## ... Similar to previous best
## Run 12 stress 9.732367e-05 
## ... Procrustes: rmse 0.0001456873  max resid 0.0003506201 
## ... Similar to previous best
## Run 13 stress 8.410429e-05 
## ... Procrustes: rmse 0.000148631  max resid 0.00052961 
## ... Similar to previous best
## Run 14 stress 9.283209e-05 
## ... Procrustes: rmse 0.0001522513  max resid 0.0005156826 
## ... Similar to previous best
## Run 15 stress 9.286035e-05 
## ... Procrustes: rmse 0.0001636369  max resid 0.0005702708 
## ... Similar to previous best
## Run 16 stress 9.781194e-05 
## ... Procrustes: rmse 0.0001666595  max resid 0.0006708884 
## ... Similar to previous best
## Run 17 stress 9.049256e-05 
## ... Procrustes: rmse 0.0001588367  max resid 0.000493547 
## ... Similar to previous best
## Run 18 stress 8.199813e-05 
## ... Procrustes: rmse 0.0001399481  max resid 0.0005576346 
## ... Similar to previous best
## Run 19 stress 8.250146e-05 
## ... Procrustes: rmse 0.000136241  max resid 0.0004024118 
## ... Similar to previous best
## Run 20 stress 9.571733e-05 
## ... Procrustes: rmse 0.0001496826  max resid 0.0004840441 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.744838e-05 
## ... Procrustes: rmse 0.0001694317  max resid 0.000744948 
## ... Similar to previous best
## Run 2 stress 9.08163e-05 
## ... Procrustes: rmse 0.0001770082  max resid 0.0008968553 
## ... Similar to previous best
## Run 3 stress 9.091627e-05 
## ... Procrustes: rmse 0.0001683905  max resid 0.0008076063 
## ... Similar to previous best
## Run 4 stress 9.054761e-05 
## ... Procrustes: rmse 0.0001759863  max resid 0.0009284688 
## ... Similar to previous best
## Run 5 stress 9.918251e-05 
## ... Procrustes: rmse 0.0001947961  max resid 0.001057226 
## ... Similar to previous best
## Run 6 stress 9.746803e-05 
## ... Procrustes: rmse 0.000179102  max resid 0.0007914789 
## ... Similar to previous best
## Run 7 stress 9.43766e-05 
## ... Procrustes: rmse 0.0001856724  max resid 0.0007778767 
## ... Similar to previous best
## Run 8 stress 9.621068e-05 
## ... Procrustes: rmse 0.0001824436  max resid 0.0006879437 
## ... Similar to previous best
## Run 9 stress 8.361984e-05 
## ... Procrustes: rmse 0.0001679514  max resid 0.0007159564 
## ... Similar to previous best
## Run 10 stress 9.089442e-05 
## ... Procrustes: rmse 0.0001640219  max resid 0.0008387327 
## ... Similar to previous best
## Run 11 stress 9.22039e-05 
## ... Procrustes: rmse 0.0001735072  max resid 0.000949042 
## ... Similar to previous best
## Run 12 stress 9.270314e-05 
## ... Procrustes: rmse 0.0001711752  max resid 0.001001346 
## ... Similar to previous best
## Run 13 stress 9.373353e-05 
## ... Procrustes: rmse 0.0001792234  max resid 0.0009369313 
## ... Similar to previous best
## Run 14 stress 9.570845e-05 
## ... Procrustes: rmse 0.0001688608  max resid 0.0007430867 
## ... Similar to previous best
## Run 15 stress 9.931906e-05 
## ... Procrustes: rmse 0.0001795798  max resid 0.0009777482 
## ... Similar to previous best
## Run 16 stress 9.936983e-05 
## ... Procrustes: rmse 0.0001840853  max resid 0.0008745316 
## ... Similar to previous best
## Run 17 stress 7.460065e-05 
## ... Procrustes: rmse 0.0001526369  max resid 0.0008466613 
## ... Similar to previous best
## Run 18 stress 9.990659e-05 
## ... Procrustes: rmse 0.0001922711  max resid 0.001027854 
## ... Similar to previous best
## Run 19 stress 9.476789e-05 
## ... Procrustes: rmse 0.0001762121  max resid 0.000721772 
## ... Similar to previous best
## Run 20 stress 9.178347e-05 
## ... Procrustes: rmse 0.0001626659  max resid 0.0004904969 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 8.991263e-05 
## ... Procrustes: rmse 0.0001478254  max resid 0.0005231353 
## ... Similar to previous best
## Run 2 stress 9.865867e-05 
## ... Procrustes: rmse 0.0001498493  max resid 0.0004562479 
## ... Similar to previous best
## Run 3 stress 9.908485e-05 
## ... Procrustes: rmse 0.0001554751  max resid 0.000548006 
## ... Similar to previous best
## Run 4 stress 9.343688e-05 
## ... Procrustes: rmse 0.0001517385  max resid 0.000570355 
## ... Similar to previous best
## Run 5 stress 8.629799e-05 
## ... Procrustes: rmse 0.0001364997  max resid 0.000509679 
## ... Similar to previous best
## Run 6 stress 9.995289e-05 
## ... Procrustes: rmse 0.000159967  max resid 0.0006399464 
## ... Similar to previous best
## Run 7 stress 9.700121e-05 
## ... Procrustes: rmse 0.0001503632  max resid 0.0008089796 
## ... Similar to previous best
## Run 8 stress 9.123543e-05 
## ... Procrustes: rmse 0.000147353  max resid 0.0007493319 
## ... Similar to previous best
## Run 9 stress 9.900296e-05 
## ... Procrustes: rmse 0.000153357  max resid 0.0006162373 
## ... Similar to previous best
## Run 10 stress 9.305477e-05 
## ... Procrustes: rmse 0.0001560069  max resid 0.0006535648 
## ... Similar to previous best
## Run 11 stress 9.835633e-05 
## ... Procrustes: rmse 0.0001541081  max resid 0.000540582 
## ... Similar to previous best
## Run 12 stress 8.880932e-05 
## ... Procrustes: rmse 0.0001544345  max resid 0.000518712 
## ... Similar to previous best
## Run 13 stress 9.836139e-05 
## ... Procrustes: rmse 0.0001752034  max resid 0.0006316572 
## ... Similar to previous best
## Run 14 stress 9.870466e-05 
## ... Procrustes: rmse 0.0001800887  max resid 0.0006788707 
## ... Similar to previous best
## Run 15 stress 9.183838e-05 
## ... Procrustes: rmse 0.0001384013  max resid 0.0006547405 
## ... Similar to previous best
## Run 16 stress 9.268203e-05 
## ... Procrustes: rmse 0.000154087  max resid 0.0004575641 
## ... Similar to previous best
## Run 17 stress 8.753984e-05 
## ... Procrustes: rmse 0.0001473285  max resid 0.0007263853 
## ... Similar to previous best
## Run 18 stress 8.997578e-05 
## ... Procrustes: rmse 0.0001537794  max resid 0.0006338977 
## ... Similar to previous best
## Run 19 stress 9.81983e-05 
## ... Procrustes: rmse 0.0001468926  max resid 0.0005781092 
## ... Similar to previous best
## Run 20 stress 8.264598e-05 
## ... Procrustes: rmse 0.0001508773  max resid 0.0007577829 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 9.928109e-05 
## ... Procrustes: rmse 0.0001901847  max resid 0.0006640892 
## ... Similar to previous best
## Run 2 stress 9.861233e-05 
## ... Procrustes: rmse 0.0002046389  max resid 0.0008075977 
## ... Similar to previous best
## Run 3 stress 9.312531e-05 
## ... Procrustes: rmse 0.000179873  max resid 0.0008867971 
## ... Similar to previous best
## Run 4 stress 9.89407e-05 
## ... Procrustes: rmse 0.0002005398  max resid 0.001088059 
## ... Similar to previous best
## Run 5 stress 9.782362e-05 
## ... Procrustes: rmse 0.0002261366  max resid 0.00122972 
## ... Similar to previous best
## Run 6 stress 9.788952e-05 
## ... Procrustes: rmse 0.0002265095  max resid 0.001222707 
## ... Similar to previous best
## Run 7 stress 9.912394e-05 
## ... Procrustes: rmse 0.0001823685  max resid 0.001112316 
## ... Similar to previous best
## Run 8 stress 9.678591e-05 
## ... Procrustes: rmse 0.0001966802  max resid 0.0009612072 
## ... Similar to previous best
## Run 9 stress 8.871242e-05 
## ... Procrustes: rmse 0.0001865244  max resid 0.0009401972 
## ... Similar to previous best
## Run 10 stress 9.440076e-05 
## ... Procrustes: rmse 0.0002265606  max resid 0.001269255 
## ... Similar to previous best
## Run 11 stress 9.814904e-05 
## ... Procrustes: rmse 0.0002354599  max resid 0.001143231 
## ... Similar to previous best
## Run 12 stress 9.115829e-05 
## ... Procrustes: rmse 0.0001736362  max resid 0.0006847871 
## ... Similar to previous best
## Run 13 stress 8.011186e-05 
## ... Procrustes: rmse 0.0001793137  max resid 0.0009517767 
## ... Similar to previous best
## Run 14 stress 9.856441e-05 
## ... Procrustes: rmse 0.0001927279  max resid 0.0008431198 
## ... Similar to previous best
## Run 15 stress 8.599339e-05 
## ... Procrustes: rmse 0.0001269807  max resid 0.0005250521 
## ... Similar to previous best
## Run 16 stress 9.415137e-05 
## ... Procrustes: rmse 0.000194021  max resid 0.001073199 
## ... Similar to previous best
## Run 17 stress 9.368113e-05 
## ... Procrustes: rmse 0.000195539  max resid 0.001088761 
## ... Similar to previous best
## Run 18 stress 9.449807e-05 
## ... Procrustes: rmse 0.0001520591  max resid 0.0005189785 
## ... Similar to previous best
## Run 19 stress 9.338985e-05 
## ... Procrustes: rmse 0.0001873373  max resid 0.0006348992 
## ... Similar to previous best
## Run 20 stress 9.03748e-05 
## ... Procrustes: rmse 0.0001843697  max resid 0.0009679146 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0001042102 
## ... Procrustes: rmse 0.0004061777  max resid 0.002073754 
## ... Similar to previous best
## Run 2 stress 9.94146e-05 
## ... Procrustes: rmse 0.000352511  max resid 0.001585636 
## ... Similar to previous best
## Run 3 stress 0.0001036477 
## ... Procrustes: rmse 0.0003894654  max resid 0.002758619 
## ... Similar to previous best
## Run 4 stress 9.896826e-05 
## ... Procrustes: rmse 0.0003612628  max resid 0.002123 
## ... Similar to previous best
## Run 5 stress 0.0001140364 
## ... Procrustes: rmse 0.0004485065  max resid 0.002889977 
## ... Similar to previous best
## Run 6 stress 9.69481e-05 
## ... Procrustes: rmse 0.0003380018  max resid 0.001478861 
## ... Similar to previous best
## Run 7 stress 0.0001239074 
## ... Procrustes: rmse 0.0004627741  max resid 0.002888351 
## ... Similar to previous best
## Run 8 stress 0.000104301 
## ... Procrustes: rmse 0.0004127469  max resid 0.002557512 
## ... Similar to previous best
## Run 9 stress 0.0001042099 
## ... Procrustes: rmse 0.0003938876  max resid 0.002767697 
## ... Similar to previous best
## Run 10 stress 0.000167714 
## ... Procrustes: rmse 0.0005297217  max resid 0.003775653 
## ... Similar to previous best
## Run 11 stress 0.0001115175 
## ... Procrustes: rmse 0.0004342985  max resid 0.002698302 
## ... Similar to previous best
## Run 12 stress 0.0001069778 
## ... Procrustes: rmse 0.0004253061  max resid 0.00240873 
## ... Similar to previous best
## Run 13 stress 0.0001127099 
## ... Procrustes: rmse 0.000420037  max resid 0.002870787 
## ... Similar to previous best
## Run 14 stress 8.570445e-05 
## ... Procrustes: rmse 0.0003040533  max resid 0.001814368 
## ... Similar to previous best
## Run 15 stress 0.0001143883 
## ... Procrustes: rmse 0.0004438942  max resid 0.002562706 
## ... Similar to previous best
## Run 16 stress 0.0001135705 
## ... Procrustes: rmse 0.0004095298  max resid 0.002867028 
## ... Similar to previous best
## Run 17 stress 0.0001200141 
## ... Procrustes: rmse 0.0004506632  max resid 0.002752666 
## ... Similar to previous best
## Run 18 stress 0.000111803 
## ... Procrustes: rmse 0.0004349329  max resid 0.002664416 
## ... Similar to previous best
## Run 19 stress 0.0001083401 
## ... Procrustes: rmse 0.0004271084  max resid 0.002293266 
## ... Similar to previous best
## Run 20 stress 0.0001107156 
## ... Procrustes: rmse 0.0004347005  max resid 0.002594828 
## ... Similar to previous best
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0004054395 
## ... Procrustes: rmse 0.004676715  max resid 0.01356454 
## Run 2 stress 0.0005082604 
## Run 3 stress 0.0004280112 
## ... Procrustes: rmse 0.004990536  max resid 0.01377029 
## Run 4 stress 0.0004174721 
## ... Procrustes: rmse 0.004771636  max resid 0.01247505 
## Run 5 stress 0.0004501231 
## ... Procrustes: rmse 0.004992105  max resid 0.01680338 
## Run 6 stress 0.0005188257 
## Run 7 stress 0.0004800901 
## ... Procrustes: rmse 0.005044465  max resid 0.01408516 
## Run 8 stress 0.0004609701 
## ... Procrustes: rmse 0.005095727  max resid 0.01770976 
## Run 9 stress 0.0004409208 
## ... Procrustes: rmse 0.005070787  max resid 0.01507456 
## Run 10 stress 0.0004810374 
## ... Procrustes: rmse 0.005176887  max resid 0.01507412 
## Run 11 stress 0.0004990449 
## ... Procrustes: rmse 0.005464092  max resid 0.01339958 
## Run 12 stress 0.0004792089 
## ... Procrustes: rmse 0.005529758  max resid 0.01809657 
## Run 13 stress 0.0006216051 
## Run 14 stress 0.0004399177 
## ... Procrustes: rmse 0.0049744  max resid 0.01187789 
## Run 15 stress 0.0004277511 
## ... Procrustes: rmse 0.004882496  max resid 0.0141324 
## Run 16 stress 0.0005071531 
## Run 17 stress 0.0005416278 
## Run 18 stress 0.0005301443 
## Run 19 stress 0.0004718996 
## ... Procrustes: rmse 0.005223629  max resid 0.01485867 
## Run 20 stress 0.0005888216 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0003770903 
## ... Procrustes: rmse 0.004647337  max resid 0.01277051 
## Run 2 stress 0.0003595577 
## ... Procrustes: rmse 0.004466133  max resid 0.0115391 
## Run 3 stress 0.0006634805 
## Run 4 stress 0.0006770347 
## Run 5 stress 0.0004441678 
## ... Procrustes: rmse 0.004853688  max resid 0.01298301 
## Run 6 stress 0.0003498852 
## ... Procrustes: rmse 0.004342325  max resid 0.009651038 
## ... Similar to previous best
## Run 7 stress 0.0004049592 
## ... Procrustes: rmse 0.004712413  max resid 0.01214893 
## Run 8 stress 0.0007520971 
## Run 9 stress 0.0004388818 
## ... Procrustes: rmse 0.00487844  max resid 0.01374855 
## Run 10 stress 0.0005211211 
## Run 11 stress 0.0004787295 
## ... Procrustes: rmse 0.004842006  max resid 0.01478272 
## Run 12 stress 0.0006515084 
## Run 13 stress 0.0006826402 
## Run 14 stress 0.0005924982 
## Run 15 stress 0.0004114997 
## ... Procrustes: rmse 0.004798863  max resid 0.01258189 
## Run 16 stress 0.0004281542 
## ... Procrustes: rmse 0.004695837  max resid 0.01135825 
## Run 17 stress 0.0005549326 
## Run 18 stress 0.0003579141 
## ... Procrustes: rmse 0.004333386  max resid 0.00984619 
## ... Similar to previous best
## Run 19 stress 0.0004275255 
## ... Procrustes: rmse 0.00494641  max resid 0.0135284 
## Run 20 stress 0.0005938215 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0004447637 
## ... Procrustes: rmse 0.005078614  max resid 0.01613304 
## Run 2 stress 0.0004033047 
## ... Procrustes: rmse 0.004892495  max resid 0.01381883 
## Run 3 stress 0.0005755525 
## Run 4 stress 0.0004064063 
## ... Procrustes: rmse 0.004795635  max resid 0.01242594 
## Run 5 stress 0.0004762347 
## ... Procrustes: rmse 0.005164971  max resid 0.02205592 
## Run 6 stress 0.0006007723 
## Run 7 stress 0.0004128966 
## ... Procrustes: rmse 0.004511226  max resid 0.01001045 
## Run 8 stress 0.0004368608 
## ... Procrustes: rmse 0.004929261  max resid 0.01115851 
## Run 9 stress 0.0004084051 
## ... Procrustes: rmse 0.004661014  max resid 0.01171382 
## Run 10 stress 0.001269329 
## Run 11 stress 0.0004188099 
## ... Procrustes: rmse 0.004764357  max resid 0.01453556 
## Run 12 stress 0.0006148549 
## Run 13 stress 0.000608749 
## Run 14 stress 0.0005076747 
## Run 15 stress 0.0005376589 
## Run 16 stress 0.0006209523 
## Run 17 stress 0.0005245442 
## Run 18 stress 0.0004501203 
## ... Procrustes: rmse 0.005044045  max resid 0.01586529 
## Run 19 stress 0.0004712087 
## ... Procrustes: rmse 0.005024777  max resid 0.01140351 
## Run 20 stress 0.0004269802 
## ... Procrustes: rmse 0.004760687  max resid 0.01099811 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0005749425 
## Run 2 stress 0.0004620371 
## ... Procrustes: rmse 0.005062215  max resid 0.01387258 
## Run 3 stress 0.0006354683 
## Run 4 stress 0.0004485594 
## ... Procrustes: rmse 0.004762857  max resid 0.01124355 
## Run 5 stress 0.0003695395 
## ... Procrustes: rmse 0.004447122  max resid 0.009093954 
## ... Similar to previous best
## Run 6 stress 0.0004044759 
## ... Procrustes: rmse 0.004524124  max resid 0.01587895 
## Run 7 stress 0.0006280256 
## Run 8 stress 0.0005507887 
## Run 9 stress 0.0005085121 
## Run 10 stress 0.0004221184 
## ... Procrustes: rmse 0.004849176  max resid 0.01181672 
## Run 11 stress 0.0006176691 
## Run 12 stress 0.0003491385 
## ... Procrustes: rmse 0.004352353  max resid 0.01093186 
## Run 13 stress 0.0004344122 
## ... Procrustes: rmse 0.00477226  max resid 0.01124328 
## Run 14 stress 0.0004069835 
## ... Procrustes: rmse 0.00479846  max resid 0.0139211 
## Run 15 stress 0.0005679287 
## Run 16 stress 0.0004479994 
## ... Procrustes: rmse 0.005179643  max resid 0.01592984 
## Run 17 stress 0.0005469223 
## Run 18 stress 0.0005964285 
## Run 19 stress 0.0003946412 
## ... Procrustes: rmse 0.004552976  max resid 0.01107987 
## Run 20 stress 0.0005981234 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.001020822 
## Run 2 stress 0.0006444083 
## Run 3 stress 0.0004469618 
## ... Procrustes: rmse 0.005075876  max resid 0.01537029 
## Run 4 stress 0.0004723572 
## ... Procrustes: rmse 0.005179591  max resid 0.0180244 
## Run 5 stress 0.000871568 
## Run 6 stress 0.0004267588 
## ... Procrustes: rmse 0.004685492  max resid 0.01408312 
## Run 7 stress 0.0004450017 
## ... Procrustes: rmse 0.004849129  max resid 0.01216869 
## Run 8 stress 0.00062076 
## Run 9 stress 0.000499895 
## ... Procrustes: rmse 0.005518242  max resid 0.0156967 
## Run 10 stress 0.0004544183 
## ... Procrustes: rmse 0.005000542  max resid 0.01421862 
## Run 11 stress 0.0003944085 
## ... Procrustes: rmse 0.004785272  max resid 0.01191196 
## Run 12 stress 0.0004193852 
## ... Procrustes: rmse 0.004763153  max resid 0.01356063 
## Run 13 stress 0.0004010218 
## ... Procrustes: rmse 0.004554851  max resid 0.01091679 
## Run 14 stress 0.0004299752 
## ... Procrustes: rmse 0.004965562  max resid 0.01203504 
## Run 15 stress 0.0004098858 
## ... Procrustes: rmse 0.004775098  max resid 0.01452086 
## Run 16 stress 0.0004102211 
## ... Procrustes: rmse 0.004758659  max resid 0.01438049 
## Run 17 stress 0.0003788778 
## ... Procrustes: rmse 0.004844282  max resid 0.013958 
## Run 18 stress 0.0004917145 
## ... Procrustes: rmse 0.005279683  max resid 0.01222148 
## Run 19 stress 0.0008179319 
## Run 20 stress 0.0004495055 
## ... Procrustes: rmse 0.005361393  max resid 0.01561308 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0004674618 
## ... Procrustes: rmse 0.004993136  max resid 0.01404296 
## Run 2 stress 0.0005291951 
## Run 3 stress 0.0004861855 
## ... Procrustes: rmse 0.005080865  max resid 0.01607966 
## Run 4 stress 0.0005611245 
## Run 5 stress 0.0004406592 
## ... Procrustes: rmse 0.004866496  max resid 0.01324931 
## Run 6 stress 0.0005615114 
## Run 7 stress 0.0005579774 
## Run 8 stress 0.000455977 
## ... Procrustes: rmse 0.004956591  max resid 0.01065272 
## Run 9 stress 0.0009508129 
## Run 10 stress 0.000451864 
## ... Procrustes: rmse 0.005054561  max resid 0.01316836 
## Run 11 stress 0.0005998938 
## Run 12 stress 0.0004366676 
## ... Procrustes: rmse 0.00496106  max resid 0.01772132 
## Run 13 stress 0.0004610555 
## ... Procrustes: rmse 0.00528373  max resid 0.01265275 
## Run 14 stress 0.0004903739 
## ... Procrustes: rmse 0.005196814  max resid 0.01870899 
## Run 15 stress 0.0004200443 
## ... Procrustes: rmse 0.005120945  max resid 0.01469275 
## Run 16 stress 0.0004318964 
## ... Procrustes: rmse 0.005042318  max resid 0.01593559 
## Run 17 stress 0.0004448968 
## ... Procrustes: rmse 0.00502414  max resid 0.01125154 
## Run 18 stress 0.0004420372 
## ... Procrustes: rmse 0.005051202  max resid 0.01423761 
## Run 19 stress 0.0003928807 
## ... Procrustes: rmse 0.004535274  max resid 0.01021824 
## Run 20 stress 0.0004641952 
## ... Procrustes: rmse 0.005423835  max resid 0.01680702 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.001306396 
## Run 2 stress 0.0004425689 
## ... Procrustes: rmse 0.005008464  max resid 0.01766338 
## Run 3 stress 0.001022519 
## Run 4 stress 0.0008608258 
## Run 5 stress 0.0004855321 
## ... Procrustes: rmse 0.006074671  max resid 0.02484161 
## Run 6 stress 0.0004107912 
## ... Procrustes: rmse 0.004614349  max resid 0.02015461 
## Run 7 stress 0.0007587915 
## Run 8 stress 0.000866098 
## Run 9 stress 0.0004721406 
## ... Procrustes: rmse 0.005032889  max resid 0.01223533 
## Run 10 stress 0.0005079859 
## Run 11 stress 0.0004634788 
## ... Procrustes: rmse 0.005321765  max resid 0.0183867 
## Run 12 stress 0.000465072 
## ... Procrustes: rmse 0.005371227  max resid 0.01475996 
## Run 13 stress 0.0007384817 
## Run 14 stress 0.000394824 
## ... Procrustes: rmse 0.004605859  max resid 0.01188218 
## Run 15 stress 0.000518258 
## Run 16 stress 0.0005136734 
## Run 17 stress 0.000473039 
## ... Procrustes: rmse 0.005138637  max resid 0.01622302 
## Run 18 stress 0.0005788303 
## Run 19 stress 0.0004015713 
## ... Procrustes: rmse 0.005131142  max resid 0.01933418 
## Run 20 stress 0.0007347459 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0003821989 
## ... Procrustes: rmse 0.004476456  max resid 0.01095567 
## Run 2 stress 0.0004461684 
## ... Procrustes: rmse 0.004955654  max resid 0.01499453 
## Run 3 stress 0.0003668378 
## ... Procrustes: rmse 0.004393967  max resid 0.008933754 
## ... Similar to previous best
## Run 4 stress 0.0006056404 
## Run 5 stress 0.0004126129 
## ... Procrustes: rmse 0.004513838  max resid 0.009770411 
## ... Similar to previous best
## Run 6 stress 0.0004918153 
## ... Procrustes: rmse 0.005465414  max resid 0.0160581 
## Run 7 stress 0.0004549366 
## ... Procrustes: rmse 0.004693527  max resid 0.01213237 
## Run 8 stress 0.000529182 
## Run 9 stress 0.0005141795 
## Run 10 stress 0.0005082289 
## Run 11 stress 0.0003903534 
## ... Procrustes: rmse 0.00452944  max resid 0.0119541 
## Run 12 stress 0.0005189809 
## Run 13 stress 0.0004385049 
## ... Procrustes: rmse 0.004698398  max resid 0.01237512 
## Run 14 stress 0.0006229466 
## Run 15 stress 0.0003581857 
## ... Procrustes: rmse 0.004201118  max resid 0.01099654 
## Run 16 stress 0.0005436673 
## Run 17 stress 0.0004776069 
## ... Procrustes: rmse 0.005053746  max resid 0.01297039 
## Run 18 stress 0.0004772436 
## ... Procrustes: rmse 0.005025857  max resid 0.01216691 
## Run 19 stress 0.0003721602 
## ... Procrustes: rmse 0.004270967  max resid 0.009809534 
## ... Similar to previous best
## Run 20 stress 0.0005126607 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0004019234 
## ... Procrustes: rmse 0.004533444  max resid 0.01234633 
## Run 2 stress 0.0005133353 
## Run 3 stress 0.0005655076 
## Run 4 stress 0.0005768717 
## Run 5 stress 0.000478123 
## ... Procrustes: rmse 0.004954507  max resid 0.01271203 
## Run 6 stress 0.0008374938 
## Run 7 stress 0.0005370092 
## Run 8 stress 0.0006193657 
## Run 9 stress 0.0006861016 
## Run 10 stress 0.0005618969 
## Run 11 stress 0.0006143793 
## Run 12 stress 0.0004406319 
## ... Procrustes: rmse 0.005194143  max resid 0.01424841 
## Run 13 stress 0.0005161696 
## Run 14 stress 0.0005661574 
## Run 15 stress 0.00041776 
## ... Procrustes: rmse 0.004988723  max resid 0.01321047 
## Run 16 stress 0.0004606636 
## ... Procrustes: rmse 0.004861812  max resid 0.01231159 
## Run 17 stress 0.0004377342 
## ... Procrustes: rmse 0.005055119  max resid 0.01654559 
## Run 18 stress 0.0004524103 
## ... Procrustes: rmse 0.005285869  max resid 0.01770919 
## Run 19 stress 0.0003976137 
## ... Procrustes: rmse 0.004718745  max resid 0.014156 
## Run 20 stress 0.0004927219 
## ... Procrustes: rmse 0.005525857  max resid 0.01672111 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0004193772 
## ... Procrustes: rmse 0.004686056  max resid 0.01276435 
## Run 2 stress 0.0004221538 
## ... Procrustes: rmse 0.004828868  max resid 0.01339936 
## Run 3 stress 0.0004318669 
## ... Procrustes: rmse 0.004855748  max resid 0.01373132 
## Run 4 stress 0.0004504515 
## ... Procrustes: rmse 0.004998023  max resid 0.01238517 
## Run 5 stress 0.0005695926 
## Run 6 stress 0.0004079489 
## ... Procrustes: rmse 0.004671392  max resid 0.01494327 
## Run 7 stress 0.0006315154 
## Run 8 stress 0.0004025266 
## ... Procrustes: rmse 0.004764022  max resid 0.01296106 
## Run 9 stress 0.0004376535 
## ... Procrustes: rmse 0.004996028  max resid 0.0138257 
## Run 10 stress 0.0005060977 
## Run 11 stress 0.0005937262 
## Run 12 stress 0.0004900329 
## ... Procrustes: rmse 0.005242864  max resid 0.01562874 
## Run 13 stress 0.0005332133 
## Run 14 stress 0.0005381253 
## Run 15 stress 0.0005295212 
## Run 16 stress 0.0004312233 
## ... Procrustes: rmse 0.004691479  max resid 0.01056047 
## Run 17 stress 0.0003927881 
## ... Procrustes: rmse 0.00454853  max resid 0.009918742 
## ... Similar to previous best
## Run 18 stress 0.0006719391 
## Run 19 stress 0.0005363235 
## Run 20 stress 0.00074983 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0005236368 
## Run 2 stress 0.0009755487 
## Run 3 stress 0.0004721384 
## ... Procrustes: rmse 0.005674737  max resid 0.02545835 
## Run 4 stress 0.0006257409 
## Run 5 stress 0.0003957379 
## ... Procrustes: rmse 0.004788155  max resid 0.0123255 
## Run 6 stress 0.0006845759 
## Run 7 stress 0.0006755215 
## Run 8 stress 0.0005303393 
## Run 9 stress 0.0003979002 
## ... Procrustes: rmse 0.005083971  max resid 0.01845139 
## Run 10 stress 0.000395574 
## ... Procrustes: rmse 0.00459981  max resid 0.01194673 
## Run 11 stress 0.0003540009 
## ... Procrustes: rmse 0.004765595  max resid 0.01826128 
## Run 12 stress 0.0003955707 
## ... Procrustes: rmse 0.004608488  max resid 0.01080273 
## Run 13 stress 0.0004512104 
## ... Procrustes: rmse 0.005486612  max resid 0.02081706 
## Run 14 stress 0.0005456189 
## Run 15 stress 0.0004532211 
## ... Procrustes: rmse 0.004930553  max resid 0.01187482 
## Run 16 stress 0.0004728354 
## ... Procrustes: rmse 0.005077693  max resid 0.01719745 
## Run 17 stress 0.000420513 
## ... Procrustes: rmse 0.004924917  max resid 0.01470531 
## Run 18 stress 0.0004211687 
## ... Procrustes: rmse 0.005344954  max resid 0.02120713 
## Run 19 stress 0.0006219744 
## Run 20 stress 0.0005985718 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0003849695 
## ... Procrustes: rmse 0.004595968  max resid 0.013751 
## Run 2 stress 0.0004080449 
## ... Procrustes: rmse 0.004639177  max resid 0.009779006 
## ... Similar to previous best
## Run 3 stress 0.0004975438 
## ... Procrustes: rmse 0.005274462  max resid 0.01487247 
## Run 4 stress 0.0005188719 
## Run 5 stress 0.0004101888 
## ... Procrustes: rmse 0.004899145  max resid 0.01232175 
## Run 6 stress 0.0007265683 
## Run 7 stress 0.0003697567 
## ... Procrustes: rmse 0.004772944  max resid 0.01615411 
## Run 8 stress 0.0004027828 
## ... Procrustes: rmse 0.004739352  max resid 0.01303041 
## Run 9 stress 0.0003969871 
## ... Procrustes: rmse 0.004579626  max resid 0.01616612 
## Run 10 stress 0.0004375693 
## ... Procrustes: rmse 0.004723532  max resid 0.01014235 
## Run 11 stress 0.0004366475 
## ... Procrustes: rmse 0.004984618  max resid 0.01427805 
## Run 12 stress 0.0004681725 
## ... Procrustes: rmse 0.005178754  max resid 0.01680358 
## Run 13 stress 0.0005118307 
## Run 14 stress 0.0005812064 
## Run 15 stress 0.0006515012 
## Run 16 stress 0.0004383101 
## ... Procrustes: rmse 0.005239162  max resid 0.01672319 
## Run 17 stress 0.0004823391 
## ... Procrustes: rmse 0.005091969  max resid 0.01552579 
## Run 18 stress 0.0003847079 
## ... Procrustes: rmse 0.004595912  max resid 0.01091414 
## Run 19 stress 0.0004241075 
## ... Procrustes: rmse 0.004843037  max resid 0.01155878 
## Run 20 stress 0.0004509059 
## ... Procrustes: rmse 0.004961292  max resid 0.01367751 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.000674973 
## Run 2 stress 0.0007877988 
## Run 3 stress 0.0005180845 
## Run 4 stress 0.0005762981 
## Run 5 stress 0.0004674005 
## ... Procrustes: rmse 0.005145946  max resid 0.01385535 
## Run 6 stress 0.001177719 
## Run 7 stress 0.0004829814 
## ... Procrustes: rmse 0.005583394  max resid 0.01620118 
## Run 8 stress 0.000422639 
## ... Procrustes: rmse 0.00473135  max resid 0.01301675 
## Run 9 stress 0.0004921124 
## ... Procrustes: rmse 0.005614911  max resid 0.02007218 
## Run 10 stress 0.0004643677 
## ... Procrustes: rmse 0.005054227  max resid 0.01115994 
## Run 11 stress 0.0004943529 
## ... Procrustes: rmse 0.005486646  max resid 0.01942662 
## Run 12 stress 0.0005188606 
## Run 13 stress 0.0004736155 
## ... Procrustes: rmse 0.005398312  max resid 0.01608717 
## Run 14 stress 0.0004765935 
## ... Procrustes: rmse 0.005104658  max resid 0.01637495 
## Run 15 stress 0.0006275954 
## Run 16 stress 0.0003944783 
## ... Procrustes: rmse 0.00486284  max resid 0.0154605 
## Run 17 stress 0.0004099759 
## ... Procrustes: rmse 0.004901942  max resid 0.01569258 
## Run 18 stress 0.000461668 
## ... Procrustes: rmse 0.005339949  max resid 0.02185588 
## Run 19 stress 0.0004353079 
## ... Procrustes: rmse 0.004951124  max resid 0.01550179 
## Run 20 stress 0.0004247351 
## ... Procrustes: rmse 0.004866573  max resid 0.01532616 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0004211627 
## ... Procrustes: rmse 0.005399464  max resid 0.01685116 
## Run 2 stress 0.0006495876 
## Run 3 stress 0.000444137 
## ... Procrustes: rmse 0.005421098  max resid 0.01621439 
## Run 4 stress 0.0004446032 
## ... Procrustes: rmse 0.004748319  max resid 0.01665641 
## Run 5 stress 0.0004420901 
## ... Procrustes: rmse 0.004938855  max resid 0.01814248 
## Run 6 stress 0.0005175497 
## Run 7 stress 0.0007217013 
## Run 8 stress 0.0006917951 
## Run 9 stress 0.0005819831 
## Run 10 stress 0.0005461722 
## Run 11 stress 0.0004619445 
## ... Procrustes: rmse 0.005074063  max resid 0.0179441 
## Run 12 stress 0.0004497957 
## ... Procrustes: rmse 0.005702384  max resid 0.02528707 
## Run 13 stress 0.000501003 
## Run 14 stress 0.0003243497 
## ... Procrustes: rmse 0.004069295  max resid 0.01006512 
## Run 15 stress 0.0004324889 
## ... Procrustes: rmse 0.005192646  max resid 0.01639804 
## Run 16 stress 0.0004780882 
## ... Procrustes: rmse 0.00542541  max resid 0.01532617 
## Run 17 stress 0.000499468 
## ... Procrustes: rmse 0.005788939  max resid 0.02298442 
## Run 18 stress 0.0005019001 
## Run 19 stress 0.0005428689 
## Run 20 stress 0.0003848443 
## ... Procrustes: rmse 0.004631369  max resid 0.01183669 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.000528101 
## Run 2 stress 0.0005477698 
## Run 3 stress 0.000476103 
## ... Procrustes: rmse 0.005213205  max resid 0.0144384 
## Run 4 stress 0.000443488 
## ... Procrustes: rmse 0.005089883  max resid 0.01617792 
## Run 5 stress 0.0004167702 
## ... Procrustes: rmse 0.004851587  max resid 0.0159724 
## Run 6 stress 0.0005855826 
## Run 7 stress 0.0005207991 
## Run 8 stress 0.0006425186 
## Run 9 stress 0.000432794 
## ... Procrustes: rmse 0.005122171  max resid 0.01475833 
## Run 10 stress 0.0005412621 
## Run 11 stress 0.0005758087 
## Run 12 stress 0.0005253865 
## Run 13 stress 0.000551593 
## Run 14 stress 0.0006039365 
## Run 15 stress 0.0009676665 
## Run 16 stress 0.0004057731 
## ... Procrustes: rmse 0.004770353  max resid 0.01082988 
## Run 17 stress 0.001054572 
## Run 18 stress 0.000597139 
## Run 19 stress 0.001421052 
## Run 20 stress 0.0005040688 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0003993857 
## ... Procrustes: rmse 0.004822579  max resid 0.01289955 
## Run 2 stress 0.001142956 
## Run 3 stress 0.0009003492 
## Run 4 stress 0.000535482 
## Run 5 stress 0.0005033666 
## Run 6 stress 0.000451072 
## ... Procrustes: rmse 0.005283965  max resid 0.01844184 
## Run 7 stress 0.0004871623 
## ... Procrustes: rmse 0.005226793  max resid 0.0161706 
## Run 8 stress 0.0007140729 
## Run 9 stress 0.000398286 
## ... Procrustes: rmse 0.00476833  max resid 0.01435978 
## Run 10 stress 0.0007189067 
## Run 11 stress 0.0007795582 
## Run 12 stress 0.0006254932 
## Run 13 stress 0.0004717136 
## ... Procrustes: rmse 0.005933248  max resid 0.02231356 
## Run 14 stress 0.0009121538 
## Run 15 stress 0.0004108764 
## ... Procrustes: rmse 0.0051609  max resid 0.01708081 
## Run 16 stress 0.0006425304 
## Run 17 stress 0.000410325 
## ... Procrustes: rmse 0.005252605  max resid 0.01688582 
## Run 18 stress 0.0005237198 
## Run 19 stress 0.00086598 
## Run 20 stress 0.0007276005 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0005155999 
## Run 2 stress 0.0004899788 
## ... Procrustes: rmse 0.005317086  max resid 0.02524392 
## Run 3 stress 0.0006053325 
## Run 4 stress 0.0005216737 
## Run 5 stress 0.0005106472 
## Run 6 stress 0.0005746181 
## Run 7 stress 0.0004764314 
## ... Procrustes: rmse 0.005104271  max resid 0.01437562 
## Run 8 stress 0.0005795286 
## Run 9 stress 0.0004601214 
## ... Procrustes: rmse 0.005346898  max resid 0.01650301 
## Run 10 stress 0.0005583001 
## Run 11 stress 0.0006328677 
## Run 12 stress 0.0003634761 
## ... Procrustes: rmse 0.004529208  max resid 0.01265819 
## Run 13 stress 0.000672465 
## Run 14 stress 0.0004430792 
## ... Procrustes: rmse 0.005067674  max resid 0.01646525 
## Run 15 stress 0.0007803134 
## Run 16 stress 0.0004252387 
## ... Procrustes: rmse 0.004777723  max resid 0.01255981 
## Run 17 stress 0.0006724624 
## Run 18 stress 0.000549138 
## Run 19 stress 0.0004753694 
## ... Procrustes: rmse 0.005501417  max resid 0.01427236 
## Run 20 stress 0.0004056256 
## ... Procrustes: rmse 0.004873396  max resid 0.01378126 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0005400356 
## Run 2 stress 0.0008055853 
## Run 3 stress 0.0004856681 
## ... Procrustes: rmse 0.005115334  max resid 0.01182241 
## Run 4 stress 0.0006126835 
## Run 5 stress 0.0005335075 
## Run 6 stress 0.0005482584 
## Run 7 stress 0.0003966436 
## ... Procrustes: rmse 0.004621982  max resid 0.01269059 
## Run 8 stress 0.000539081 
## Run 9 stress 0.000677219 
## Run 10 stress 0.000359527 
## ... Procrustes: rmse 0.004583128  max resid 0.01292521 
## Run 11 stress 0.0004860514 
## ... Procrustes: rmse 0.005336674  max resid 0.01658845 
## Run 12 stress 0.000494901 
## ... Procrustes: rmse 0.005699813  max resid 0.02235214 
## Run 13 stress 0.0005589346 
## Run 14 stress 0.0004932174 
## ... Procrustes: rmse 0.00593829  max resid 0.02157871 
## Run 15 stress 0.0004632155 
## ... Procrustes: rmse 0.005279462  max resid 0.01724422 
## Run 16 stress 0.0004649234 
## ... Procrustes: rmse 0.005571462  max resid 0.02355818 
## Run 17 stress 0.0006530129 
## Run 18 stress 0.0005403669 
## Run 19 stress 0.0004984566 
## ... Procrustes: rmse 0.005591758  max resid 0.02129321 
## Run 20 stress 0.0004563227 
## ... Procrustes: rmse 0.005074622  max resid 0.01605494 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0005494286 
## Run 2 stress 0.0005145648 
## Run 3 stress 0.0006290057 
## Run 4 stress 0.0005146115 
## Run 5 stress 0.0004219942 
## ... Procrustes: rmse 0.004729983  max resid 0.01128555 
## Run 6 stress 0.0006670187 
## Run 7 stress 0.0004061363 
## ... Procrustes: rmse 0.00454931  max resid 0.0107608 
## Run 8 stress 0.0004482543 
## ... Procrustes: rmse 0.004804847  max resid 0.01374689 
## Run 9 stress 0.0005722982 
## Run 10 stress 0.0003596983 
## ... Procrustes: rmse 0.004375209  max resid 0.01008431 
## Run 11 stress 0.0004515239 
## ... Procrustes: rmse 0.00478109  max resid 0.01365902 
## Run 12 stress 0.0005096998 
## Run 13 stress 0.0005311039 
## Run 14 stress 0.0005115606 
## Run 15 stress 0.0003897566 
## ... Procrustes: rmse 0.004648519  max resid 0.01070933 
## Run 16 stress 0.0006634143 
## Run 17 stress 0.0006131393 
## Run 18 stress 0.0006460661 
## Run 19 stress 0.0004272343 
## ... Procrustes: rmse 0.004836545  max resid 0.01030769 
## Run 20 stress 0.0004245322 
## ... Procrustes: rmse 0.004694856  max resid 0.01055333 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0004455235 
## ... Procrustes: rmse 0.005035378  max resid 0.01370612 
## Run 2 stress 0.0004840853 
## ... Procrustes: rmse 0.005431556  max resid 0.02354275 
## Run 3 stress 0.0003901781 
## ... Procrustes: rmse 0.004660615  max resid 0.01301871 
## Run 4 stress 0.0006856975 
## Run 5 stress 0.0004139996 
## ... Procrustes: rmse 0.004649353  max resid 0.01454429 
## Run 6 stress 0.0004613196 
## ... Procrustes: rmse 0.005159429  max resid 0.02318408 
## Run 7 stress 0.0004865776 
## ... Procrustes: rmse 0.005194842  max resid 0.01268464 
## Run 8 stress 0.0005549931 
## Run 9 stress 0.0005067894 
## Run 10 stress 0.0004430163 
## ... Procrustes: rmse 0.004752064  max resid 0.01338333 
## Run 11 stress 0.0004723749 
## ... Procrustes: rmse 0.005075101  max resid 0.01525391 
## Run 12 stress 0.000399265 
## ... Procrustes: rmse 0.004517802  max resid 0.01050185 
## Run 13 stress 0.0006961381 
## Run 14 stress 0.0004865672 
## ... Procrustes: rmse 0.005177302  max resid 0.01198743 
## Run 15 stress 0.000436846 
## ... Procrustes: rmse 0.004621057  max resid 0.01105262 
## Run 16 stress 0.0004985944 
## ... Procrustes: rmse 0.005374871  max resid 0.01407973 
## Run 17 stress 0.0003887923 
## ... Procrustes: rmse 0.004608321  max resid 0.00941683 
## ... Similar to previous best
## Run 18 stress 0.0005091787 
## Run 19 stress 0.0005212327 
## Run 20 stress 0.0006659852 
## *** Solution reached
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0005184044 
## Run 2 stress 0.0005011294 
## Run 3 stress 0.0004661713 
## ... Procrustes: rmse 0.0054855  max resid 0.02214306 
## Run 4 stress 0.0004749515 
## ... Procrustes: rmse 0.005281145  max resid 0.01668199 
## Run 5 stress 0.0003733597 
## ... Procrustes: rmse 0.00472797  max resid 0.01607216 
## Run 6 stress 0.0004053856 
## ... Procrustes: rmse 0.004710506  max resid 0.01696176 
## Run 7 stress 0.0005636963 
## Run 8 stress 0.0006892321 
## Run 9 stress 0.000550203 
## Run 10 stress 0.0003921546 
## ... Procrustes: rmse 0.004890505  max resid 0.01735947 
## Run 11 stress 0.0004650498 
## ... Procrustes: rmse 0.004811018  max resid 0.01952996 
## Run 12 stress 0.0005330389 
## Run 13 stress 0.0004803663 
## ... Procrustes: rmse 0.005667154  max resid 0.01670069 
## Run 14 stress 0.0007789463 
## Run 15 stress 0.001733128 
## Run 16 stress 0.0004180843 
## ... Procrustes: rmse 0.005243979  max resid 0.02302835 
## Run 17 stress 0.00077982 
## Run 18 stress 0.0005308876 
## Run 19 stress 0.0005371117 
## Run 20 stress 0.0004370248 
## ... Procrustes: rmse 0.005243395  max resid 0.01732859 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
# Note: results are hidden (too long)

6

Discuss the stress (or SStress) of each dimensional solution. Make a scree plot if you’re able.

#plot stress results

plot(c(1:5), results[21, ], type = "b", col = "blue", lwd = 3, 
     ylim = c(0, max(results)), xlab = "Dimensions", ylab = "Stress", pch = 19, 
     main = "MDS for Rural-Urban Data, Euclidean Distance")
mins <- apply(results[1:20, ], 2, min)
maxs <- apply(results[1:20, ], 2, max)
meds <- apply(results[1:20, ], 2, median)

for (i in 1:5){
  points(rep(i, 3), c(mins[i], meds[i], maxs[i]), type = "b", col = "red", lwd = 3, pch = 19)
}
legend(3.5, (.9*max(results)), c("MDS Solution", "20 Permutations"), lwd = 3, col = c("blue", "red"))

After performing multidimensional scaling for 1-5 dimensions, the above scree plot for stress illustrates an elbow at 2 dimensions. This stress level is below 10% and indicates a good fit. For 3 dimensions, the stress is below 5% and indicates an excellent fit. After 3 dimensions, random chance could result in comparable stress values.

Stress is a measure of the difference between actual pairwise distances and calculated reference distances; a lower stress indicates a better fit. As the dimensions exceeds that of the data (for 4 and 5 dimensions), the stress goes to 0.

7

Make a two dimensional plot of your MDS results.

data_ord_base.mds2 <- metaMDS(data_ord_base, k = 2, distance = "euclidean")
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0.0762502 
## Run 1 stress 0.0762502 
## ... Procrustes: rmse 6.666662e-06  max resid 4.201412e-05 
## ... Similar to previous best
## Run 2 stress 0.08193692 
## Run 3 stress 0.1104296 
## Run 4 stress 0.07130037 
## ... New best solution
## ... Procrustes: rmse 0.03267168  max resid 0.2604157 
## Run 5 stress 0.1222007 
## Run 6 stress 0.1064976 
## Run 7 stress 0.0819463 
## Run 8 stress 0.0762502 
## Run 9 stress 0.0713005 
## ... Procrustes: rmse 6.228924e-05  max resid 0.0003496877 
## ... Similar to previous best
## Run 10 stress 0.08193569 
## Run 11 stress 0.1140951 
## Run 12 stress 0.08193569 
## Run 13 stress 0.08194625 
## Run 14 stress 0.07625021 
## Run 15 stress 0.0713004 
## ... Procrustes: rmse 2.885257e-05  max resid 0.0001491525 
## ... Similar to previous best
## Run 16 stress 0.08194625 
## Run 17 stress 0.08614369 
## Run 18 stress 0.08194626 
## Run 19 stress 0.07130101 
## ... Procrustes: rmse 0.0001769265  max resid 0.000993719 
## ... Similar to previous best
## Run 20 stress 0.07130039 
## ... Procrustes: rmse 3.533542e-05  max resid 0.0001839468 
## ... Similar to previous best
## *** Solution reached
plot(data_ord_base.mds2, type = "t")

stressplot(data_ord_base.mds2)

The R-squared values seem sufficiently high with the two dimensional MDS result.

8

If possible, overlay some other continuous variable(s) to interpret your ordination axes. Calculate p-values for the overlaid additional variable(s). If you can, get some non-linear wireplots of the these overlaid variables (see examples online in R).

We can also add environmental variables to our plot.

fig <- ordiplot(data_ord_base.mds2, type = "none", cex = 1.1)
text(fig, "species", col = "red", cex = 1.1)
text(fig, "sites", col = "blue", cex = 0.8)

fit <- envfit(data_ord_base.mds2, data_ord_env, permutations = 1000)
plot(fit, col = "black", lwd = 3)

fit <- envfit(data_ord_base_ca, data_ord_env, permutations = 1000)
fit
## 
## ***VECTORS
## 
##                                         CA1      CA2     r2   Pr(>r)    
## Unemployment_Rate_2019              0.93609 -0.35176 0.2400 0.000999 ***
## Civilian_Labor_Force_2019_as_pct   -0.97424 -0.22551 0.4110 0.000999 ***
## Percent_Adults_Bachelors_or_Higher -0.99468 -0.10305 0.6962 0.000999 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 1000

The three overlaid continuous variables above are all significant with p<0.05. This is graphically suggested by the long length of the lines.

mds4 <- metaMDS(data_ord_env, distance="euclidean", k=4)
## Square root transformation
## Wisconsin double standardization
## Run 0 stress 0 
## Run 1 stress 0.0007227778 
## Run 2 stress 0.0007894462 
## Run 3 stress 0.0009252429 
## Run 4 stress 0.000754978 
## Run 5 stress 0.0007677275 
## Run 6 stress 0.0006250545 
## Run 7 stress 0.000780112 
## Run 8 stress 0.0005232291 
## Run 9 stress 0.004746901 
## Run 10 stress 0.0008708487 
## Run 11 stress 0.0007830212 
## Run 12 stress 0.0008947836 
## Run 13 stress 0.0009902119 
## Run 14 stress 0.001028639 
## Run 15 stress 0.0008125473 
## Run 16 stress 0.0005889211 
## Run 17 stress 0.0006813661 
## Run 18 stress 0.0007503506 
## Run 19 stress 0.0005297504 
## Run 20 stress 0.0006387298 
## *** No convergence -- monoMDS stopping criteria:
##     20: no. of iterations >= maxit
## Warning in metaMDS(data_ord_env, distance = "euclidean", k = 4): stress is
## (nearly) zero: you may have insufficient data
fig <- ordiplot(mds4, type = "none", cex = 1.1, main = "NMDS for COVID-19 Data")
text(fig, "species", col = "red", cex = 0.7)
text(fig, "sites", col = "black", cex = 0.7)
plot(fit)
tmp1 <- with(data_ord_env, ordisurf(mds4, Unemployment_Rate_2019, add = TRUE))
tmp2 <- with(data_ord_env, ordisurf(mds4, Percent_Adults_Bachelors_or_Higher, add = TRUE, col = "green4"))
tmp3 <- with(data_ord_env, ordisurf(mds4, Civilian_Labor_Force_2019_as_pct, add = TRUE, col = "purple"))

vis.gam(tmp1, main = "Unemployment Rate")

vis.gam(tmp2, main = "Percentage of Adults with Bachelor's or Higher")

vis.gam(tmp3, main = "Civilian Labor Force Percentage")

9

Again, assuming you have at least one additional continuous variable, perform canonical correspondence analysis.

As directed, here we’ll perform CCA – both with and without (or the other way around) the environmental variables.

data_ord_base_cca1 <- cca(data_ord_base, scale="FALSE")
data_ord_base_cca2 <- cca(data_ord_base, data_ord_env, scale="FALSE")
plot(data_ord_base_cca1, main="CCA without env")

plot(data_ord_base_cca2, main="CCA with env")

#plot(data_ord_base_cca, main = "CCA for Rural-Urban Type", type = "n")
#points(data_ord_base_cca, pch = 19, col = "red", cex = 1)
#text(data_ord_base_cca, "species", col = "blue", cex = 0.7)
#text(data_ord_base_cca, display = c("sites"), labels = rownames(data_ord_base), cex = 0.5)

(fit_cca <- envfit(data_ord_base_cca2, data_ord_env, permutations=1000))
## 
## ***VECTORS
## 
##                                         CCA1      CCA2     r2   Pr(>r)    
## Unemployment_Rate_2019              0.977760 -0.209739 0.2553 0.000999 ***
## Civilian_Labor_Force_2019_as_pct   -0.997160 -0.075256 0.4131 0.000999 ***
## Percent_Adults_Bachelors_or_Higher -0.999830 -0.018480 0.7048 0.000999 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## Permutation: free
## Number of permutations: 1000
plot(data_ord_base_cca2)
plot(fit_cca, col = "red", lwd = 3)

summary(data_ord_base_cca2)
## 
## Call:
## cca(X = data_ord_base, Y = data_ord_env, scale = "FALSE") 
## 
## Partitioning of scaled Chi-square:
##               Inertia Proportion
## Total         0.05033     1.0000
## Constrained   0.02673     0.5312
## Unconstrained 0.02360     0.4688
## 
## Eigenvalues, and their contribution to the scaled Chi-square 
## 
## Importance of components:
##                          CCA1     CCA2      CCA3     CA1     CA2      CA3
## Eigenvalue            0.02517 0.001433 0.0001286 0.01225 0.00795 0.002016
## Proportion Explained  0.50014 0.028465 0.0025542 0.24348 0.15796 0.040061
## Cumulative Proportion 0.50014 0.528601 0.5311551 0.77463 0.93259 0.972652
##                            CA4
## Eigenvalue            0.001376
## Proportion Explained  0.027348
## Cumulative Proportion 1.000000
## 
## Accumulated constrained eigenvalues
## Importance of components:
##                          CCA1     CCA2      CCA3
## Eigenvalue            0.02517 0.001433 0.0001286
## Proportion Explained  0.94160 0.053590 0.0048088
## Cumulative Proportion 0.94160 0.995191 1.0000000
## 
## Scaling 2 for species and site scores
## * Species are scaled proportional to eigenvalues
## * Sites are unscaled: weighted dispersion equal on all dimensions
## 
## 
## Species scores
## 
##                                                         CCA1     CCA2      CCA3
## Always_Wear_Mask_Survey                             -0.05278 -0.05184  0.004032
## Median_Household_Income_Percent_of_State_Total_2019 -0.09263  0.02673 -0.003443
## Percent_Poverty_2019                                 0.28361  0.01487 -0.020196
## Percent_Adults_Less_Than_HS                          0.39865 -0.01652  0.001006
## Covid_Confirmed_Cases_as_pct                         0.17152  0.06858  0.043256
##                                                          CA1      CA2       CA3
## Always_Wear_Mask_Survey                             -0.03731  0.12488 -0.002997
## Median_Household_Income_Percent_of_State_Total_2019  0.09936 -0.03903  0.005827
## Percent_Poverty_2019                                -0.22620 -0.08500  0.111714
## Percent_Adults_Less_Than_HS                         -0.16894 -0.05727 -0.102570
## Covid_Confirmed_Cases_as_pct                        -0.12422 -0.18453 -0.063076
## 
## 
## Site scores (weighted averages of species scores)
## 
##                  CCA1     CCA2      CCA3      CA1       CA2      CA3
## Alachua      -0.44270 -3.40786  -0.24161 -2.85980  0.330773  1.25210
## Baker         0.10024  4.26789   0.42300  1.55293 -0.777995  0.29274
## Bay          -0.64438  1.89645   3.41489  1.04832 -1.052120  0.56516
## Bradford      1.58692  3.23318  -4.78274 -0.08183 -1.114071  0.46772
## Brevard      -1.20371 -0.70458  -2.04920  0.64061  0.584208  0.35922
## Broward      -0.78323 -2.24673   4.48190 -0.56799  0.490985 -0.42667
## Calhoun       1.65422 -0.23416   2.50777 -0.54201 -0.193127 -0.38618
## Charlotte    -0.85407 -1.79553  -2.14568  0.79143  1.385045  0.58618
## Citrus       -0.20269 -1.81547  -3.34039  0.73548  0.866036  1.24778
## Clay         -1.44785  4.10021  -2.85479  2.36989 -0.826960  0.41909
## Collier      -1.06933  1.44385  -1.13605  0.10109 -0.693334 -1.60439
## Columbia      0.53112  3.77349   1.32211  0.49487 -1.132029  0.77115
## DeSoto        1.65614 -4.61067   1.16665 -1.24409  1.679176 -1.08893
## Dixie         1.92664  1.34252  -6.60205 -0.62286 -0.748921  1.16633
## Duval        -0.59565  0.02211   1.40287 -0.13757 -0.465944  0.39331
## Escambia     -0.27687  1.74232   1.67822 -0.22159 -0.703872  1.20944
## Flagler      -1.31372  0.20796  -4.24471  1.62497  0.553084  0.85203
## Franklin      1.27565  2.79012  -1.24754 -0.56045 -1.369445 -0.23333
## Gadsden       1.32128 -1.15008   4.38857 -1.08992 -0.501499 -0.58992
## Gilchrist     0.37703  1.16008  -4.16196  0.72436  0.130178  0.93945
## Glades        1.14550 -4.10171  -3.33032 -0.12684  1.473841 -0.30031
## Gulf          0.32654  3.40464   7.44655  0.81659 -2.320638 -0.66988
## Hamilton      2.92405  2.86542 -11.62673 -1.93242 -1.893437  3.02394
## Hardee        1.96030 -0.03744  -1.83912 -0.69453 -1.048443 -0.31393
## Hendry        2.01789 -3.18102   2.53173 -0.30451 -0.804561 -2.95680
## Hernando     -0.36066 -1.67076  -2.82344  1.06470  0.998128  0.50630
## Highlands     0.26128 -3.16753  -1.63842  0.06873  1.183650  0.38727
## Hillsborough -0.71013 -1.63661  -0.72228 -0.59068  0.236228  0.02218
## Holmes        1.70129 -1.95197   3.75463 -0.98807  0.815789 -0.73717
## Indian River -0.80417  0.13399  -2.23177  0.48561 -0.003610 -0.15747
## Jackson       1.43155 -0.29918   6.38724 -0.94451 -0.007011 -0.43450
## Jefferson     0.56973 -2.86330   2.89773 -1.17235  1.130851 -0.60445
## Lafayette     1.94225  4.61041  15.16637 -1.27467 -1.769550 -3.32407
## Lake         -0.82846 -0.95936  -0.81247  0.92437  1.089037  0.26855
## Lee          -0.79304 -0.31602  -0.35654  0.36711  0.453950 -0.39778
## Leon         -0.44762 -1.03335  -1.77355 -2.97313 -1.020685  1.87070
## Levy          0.68588 -3.08008  -3.45481 -0.10012  1.332323  1.50243
## Liberty       1.47275  1.42754   0.60829 -0.79446 -0.277589  0.99307
## Madison       2.15379  3.10521  -4.23025 -1.34032 -2.244500  1.29918
## Manatee      -0.90616  0.51169  -0.76392  0.39430  0.158330 -0.19494
## Marion       -0.01206 -0.42917  -2.30415  0.33564  0.456923  0.80712
## Martin       -1.38051 -0.43010  -0.93709  0.49063  0.525289 -0.53174
## Miami-Dade    0.30614 -1.71364  10.82034 -1.67193  0.359637 -1.97126
## Monroe       -1.31414 -2.14927   2.34747 -0.07716  0.763749  0.07965
## Nassau       -1.31454  5.01949  -2.01014  1.71006 -1.252636  0.07229
## Okaloosa     -1.03147  3.96982  -1.07972  0.72880 -0.963809  0.20686
## Okeechobee    1.13767 -4.39348   0.98386 -0.43563  1.593806 -1.01245
## Orange       -0.79477 -1.25250   0.55677 -0.56422 -0.031170 -0.22220
## Osceola      -0.26909 -2.68968   5.13622  0.14793  1.049223  0.03052
## Palm Beach   -0.95756 -1.79612   1.17823 -0.58413  0.254155 -0.87391
## Pasco        -0.80740 -2.85309  -0.58236  0.59090  1.567402  0.24828
## Pinellas     -0.99830 -3.07182   1.02956 -0.29765  1.202111  0.27183
## Polk         -0.03103 -1.74815   0.06866  0.23412  0.697029 -0.14035
## Putnam        1.25636 -2.27366  -5.04933 -0.62878  0.492432  1.52447
## St. Johns    -2.07921  5.17633  -3.83043  0.81310 -1.728165 -0.66101
## St. Lucie    -0.57847 -1.51729  -0.02183  1.10796  0.643239 -0.43374
## Santa Rosa   -1.10287  4.72538  -0.52166  1.32545 -1.239094  0.10723
## Sarasota     -1.56170 -0.88287   0.12730  0.35835  0.902196 -0.52889
## Seminole     -1.68298 -0.48667  -2.54127  0.12969  0.054256  0.43293
## Sumter       -1.31980 -0.04108  -1.78500  0.78670  0.750345 -0.72767
## Suwannee      1.05876  4.31106   0.78212  0.23530 -1.765324 -0.34052
## Taylor        1.69637  0.84303   3.43101 -0.16838 -0.384565 -0.46401
## Union         1.33550  1.95629  -0.08314  0.26188  0.379401 -0.54734
## Volusia      -0.64360 -1.35740  -2.70563  0.47984  0.739835  1.14598
## Wakulla      -0.37721  4.08455  -0.28765  1.52163 -0.774887  0.30464
## Walton       -0.69538  2.82575   1.12300  0.48687 -0.468831 -0.75593
## Washington    1.19601 -1.18162   0.88880 -0.50963  0.689445  0.59098
## 
## 
## Site constraints (linear combinations of constraining variables)
## 
##                   CCA1      CCA2      CCA3      CA1       CA2      CA3
## Alachua      -2.007956 -0.002997 -0.399842 -2.85980  0.330773  1.25210
## Baker         0.922848  0.890041  0.902784  1.55293 -0.777995  0.29274
## Bay          -0.084847 -1.772954  0.592189  1.04832 -1.052120  0.56516
## Bradford      1.207997  1.058849  0.995538 -0.08183 -1.114071  0.46772
## Brevard      -0.688836 -0.098129  0.142918  0.64061  0.584208  0.35922
## Broward      -0.995305 -0.641658  0.970594 -0.56799  0.490985 -0.42667
## Calhoun       1.299548 -0.122155 -0.382269 -0.54201 -0.193127 -0.38618
## Charlotte    -0.020235  0.283009 -0.982653  0.79143  1.385045  0.58618
## Citrus        0.557753 -0.969861 -2.092434  0.73548  0.866036  1.24778
## Clay         -0.197145 -0.107359  1.164709  2.36989 -0.826960  0.41909
## Collier      -1.354230  0.267885 -0.607522  0.10109 -0.693334 -1.60439
## Columbia      0.696933  0.569731  0.755388  0.49487 -1.132029  0.77115
## DeSoto        1.138442  0.585270  0.344483 -1.24409  1.679176 -1.08893
## Dixie         1.351199  0.389223 -0.060075 -0.62286 -0.748921  1.16633
## Duval        -0.721987 -0.975451  0.769796 -0.13757 -0.465944  0.39331
## Escambia     -0.393925  0.069627  0.246089 -0.22159 -0.703872  1.20944
## Flagler      -0.166712 -0.352844 -0.719791  1.62497  0.553084  0.85203
## Franklin      0.574643  0.521513 -0.125193 -0.56045 -1.369445 -0.23333
## Gadsden       0.570257 -1.149294  0.011786 -1.08992 -0.501499 -0.58992
## Gilchrist     0.858024  0.652154  0.278065  0.72436  0.130178  0.93945
## Glades        1.258029 -0.506087  0.528679 -0.12684  1.473841 -0.30031
## Gulf          0.444904 -2.698311 -0.367362  0.81659 -2.320638 -0.66988
## Hamilton      1.397363  0.529928 -0.980435 -1.93242 -1.893437  3.02394
## Hardee        1.253258 -1.481501 -1.430620 -0.69453 -1.048443 -0.31393
## Hendry        1.393228 -4.009958 -0.790186 -0.30451 -0.804561 -2.95680
## Hernando      0.530182 -0.659333 -0.817613  1.06470  0.998128  0.50630
## Highlands     0.601215 -0.760695 -1.457619  0.06873  1.183650  0.38727
## Hillsborough -1.053212 -0.450856  0.441390 -0.59068  0.236228  0.02218
## Holmes        1.263857  0.876267  0.155464 -0.98807  0.815789 -0.73717
## Indian River -0.546316 -0.293234 -1.144739  0.48561 -0.003610 -0.15747
## Jackson       0.945306  0.485231 -0.005222 -0.94451 -0.007011 -0.43450
## Jefferson     0.092725  0.825488 -0.363288 -1.17235  1.130851 -0.60445
## Lafayette     0.756734  2.215306 -0.388922 -1.27467 -1.769550 -3.32407
## Lake         -0.009966  0.412752  0.248184  0.92437  1.089037  0.26855
## Lee          -0.520889  0.403451  0.042881  0.36711  0.453950 -0.39778
## Leon         -2.335794 -0.541335 -0.684923 -2.97313 -1.020685  1.87070
## Levy          0.988017 -0.273134  0.567823 -0.10012  1.332323  1.50243
## Liberty       1.065071  1.340765 -0.798182 -0.79446 -0.277589  0.99307
## Madison       0.867993 -0.465183  0.385345 -1.34032 -2.244500  1.29918
## Manatee      -0.661535  0.516213 -0.210707  0.39430  0.158330 -0.19494
## Marion        0.350330  0.080264 -0.686281  0.33564  0.456923  0.80712
## Martin       -1.034645  0.355132 -0.395475  0.49063  0.525289 -0.53174
## Miami-Dade   -0.656128  0.877023  1.313950 -1.67193  0.359637 -1.97126
## Monroe       -1.202339 -0.400639  2.963260 -0.07716  0.763749  0.07965
## Nassau       -0.567587  0.591939  0.341978  1.71006 -1.252636  0.07229
## Okaloosa     -0.790901  1.113859  0.119242  0.72880 -0.963809  0.20686
## Okeechobee    1.091179 -0.207662  1.140160 -0.43563  1.593806 -1.01245
## Orange       -1.191455 -0.644449  1.058354 -0.56422 -0.031170 -0.22220
## Osceola       0.145779 -0.756823  1.364936  0.14793  1.049223  0.03052
## Palm Beach   -1.330926 -0.477918 -0.338012 -0.58413  0.254155 -0.87391
## Pasco        -0.082094 -0.112526 -0.078787  0.59090  1.567402  0.24828
## Pinellas     -0.882716 -0.236182  0.647977 -0.29765  1.202111  0.27183
## Polk          0.250653 -0.446754  0.049231  0.23412  0.697029 -0.14035
## Putnam        1.037210 -0.715389 -0.546727 -0.62878  0.492432  1.52447
## St. Johns    -2.100531  0.890748 -0.620499  0.81310 -1.728165 -0.66101
## St. Lucie     0.196923 -1.166346  0.217540  1.10796  0.643239 -0.43374
## Santa Rosa   -0.545711  0.637809  0.042468  1.32545 -1.239094  0.10723
## Sarasota     -1.176335  0.780044 -0.981018  0.35835  0.902196 -0.52889
## Seminole     -1.613426 -0.471502  0.472865  0.12969  0.054256  0.43293
## Sumter       -0.681182  0.808735 -4.615416  0.78670  0.750345 -0.72767
## Suwannee      0.788376  0.307791  0.576808  0.23530 -1.765324 -0.34052
## Taylor        1.516638  0.180899  0.861904 -0.16838 -0.384565 -0.46401
## Union         1.519029  2.642363 -0.115282  0.26188  0.379401 -0.54734
## Volusia      -0.128104 -0.398469  0.452265  0.47984  0.739835  1.14598
## Wakulla       0.406747  0.785360  1.065397  1.52163 -0.774887  0.30464
## Walton       -0.547063  1.422236 -0.247075  0.48687 -0.468831 -0.75593
## Washington    1.105397  0.681665  0.482510 -0.50963  0.689445  0.59098
## 
## 
## Biplot scores for constraining variables
## 
##                                       CCA1     CCA2     CCA3 CA1 CA2 CA3
## Unemployment_Rate_2019              0.5473 -0.60888 -0.57427   0   0   0
## Civilian_Labor_Force_2019_as_pct   -0.7554 -0.18958  0.62725   0   0   0
## Percent_Adults_Bachelors_or_Higher -0.9991  0.02401 -0.03542   0   0   0

The three overlaid continuous variables above are all significant with p<0.001. However, the continuous variables don’t have a great distribution on this plot, so the discriminating ability is probably not as helpful as what we might like.

10

Finally, write a paragraph or so comparing the methods you’ve used, discuss what conclusions you reach, etc.

The counties are well distributed across the quadrants in each of our MDS methods, and we find significance in three of our environmental variables. Our two-dimensional MDS results are robust and suggest two dimensions are likely optimal, although three dimensions could also be considered. Our results for canonical correspondence analysis (CCA) are somewhat concentrated and difficult to read. In CCA, we find substantially more variation on the second CCA axis, which is inversely related to unemployment. Although our relatively high amount of counties (67) contributes to the difficulty in discerning the plot, the CCA plot is particularly concentrated. We believe the NMDS plot in #8 with contour lines optimally illustrates the distribution of the counties and their relations to the NMDS axes and environmental variables. It conveys a lot of information in a single plot. Moreover, we can see that the contour lines are not exactly perpendicular to their respective blue dimensional axes, suggesting a more complex (non-linear) significant pattern of counties according to the environmental variables of unemployment, bachelor’s percentage, and civilian labor force percentage.